2. A binomial is a two-term polynomial.
Special Binomial Operations
3. A binomial is a two-term polynomial. Usually we use the
term for expressions of the form ax + b.
Special Binomial Operations
4. A binomial is a two-term polynomial. Usually we use the
term for expressions of the form ax + b.
A trinomial is a three term polynomial.
Special Binomial Operations
5. A binomial is a two-term polynomial. Usually we use the
term for expressions of the form ax + b.
A trinomial is a three term polynomial. Usually we use the
term for expressions of the form ax2 + bx + c.
Special Binomial Operations
6. A binomial is a two-term polynomial. Usually we use the
term for expressions of the form ax + b.
A trinomial is a three term polynomial. Usually we use the
term for expressions of the form ax2 + bx + c.
The product of two binomials is a trinomial.
(#x + #)(#x + #) = #x2 + #x + #
Special Binomial Operations
7. A binomial is a two-term polynomial. Usually we use the
term for expressions of the form ax + b.
A trinomial is a three term polynomial. Usually we use the
term for expressions of the form ax2 + bx + c.
The product of two binomials is a trinomial.
(#x + #)(#x + #) = #x2 + #x + #
Special Binomial Operations
F: To get the x2-term, multiply the two Front x-terms of the
binomials.
8. A binomial is a two-term polynomial. Usually we use the
term for expressions of the form ax + b.
A trinomial is a three term polynomial. Usually we use the
term for expressions of the form ax2 + bx + c.
The product of two binomials is a trinomial.
(#x + #)(#x + #) = #x2 + #x + #
Special Binomial Operations
F: To get the x2-term, multiply the two Front x-terms of the
binomials.
OI: To get the x-term, multiply the Outer and Inner pairs and
combine the results.
9. A binomial is a two-term polynomial. Usually we use the
term for expressions of the form ax + b.
A trinomial is a three term polynomial. Usually we use the
term for expressions of the form ax2 + bx + c.
The product of two binomials is a trinomial.
(#x + #)(#x + #) = #x2 + #x + #
Special Binomial Operations
F: To get the x2-term, multiply the two Front x-terms of the
binomials.
OI: To get the x-term, multiply the Outer and Inner pairs and
combine the results.
L: To get the constant term, multiply the two Last constant
terms.
10. A binomial is a two-term polynomial. Usually we use the
term for expressions of the form ax + b.
A trinomial is a three term polynomial. Usually we use the
term for expressions of the form ax2 + bx + c.
The product of two binomials is a trinomial.
(#x + #)(#x + #) = #x2 + #x + #
Special Binomial Operations
F: To get the x2-term, multiply the two Front x-terms of the
binomials.
OI: To get the x-term, multiply the Outer and Inner pairs and
combine the results.
L: To get the constant term, multiply the two Last constant
terms.
This is called the FOIL method.
11. A binomial is a two-term polynomial. Usually we use the
term for expressions of the form ax + b.
A trinomial is a three term polynomial. Usually we use the
term for expressions of the form ax2 + bx + c.
The product of two binomials is a trinomial.
(#x + #)(#x + #) = #x2 + #x + #
Special Binomial Operations
F: To get the x2-term, multiply the two Front x-terms of the
binomials.
OI: To get the x-term, multiply the Outer and Inner pairs and
combine the results.
L: To get the constant term, multiply the two Last constant
terms.
This is called the FOIL method.
The FOIL method speeds up the multiplication of above
binomial products and this will come in handy later.
12. Example A. Multiply using FOIL method.
a. (x + 3)(x – 4)
Special Binomial Operations
13. Example A. Multiply using FOIL method.
a. (x + 3)(x – 4) = x2
Special Binomial Operations
The front terms: x2-term
14. Example A. Multiply using FOIL method.
a. (x + 3)(x – 4) = x2
Special Binomial Operations
Outer pair: –4x
15. Example A. Multiply using FOIL method.
a. (x + 3)(x – 4) = x2
Special Binomial Operations
Inner pair: –4x + 3x
16. Example A. Multiply using FOIL method.
a. (x + 3)(x – 4) = x2 – x
Special Binomial Operations
Outer Inner pairs: –4x + 3x = –x
17. Example A. Multiply using FOIL method.
a. (x + 3)(x – 4) = x2 – x – 12
Special Binomial Operations
The last terms: –12
18. Special Binomial Operations
b. (3x + 4)(–2x + 5)
Example A. Multiply using FOIL method.
a. (x + 3)(x – 4) = x2 – x – 12
The last terms: –12
19. Special Binomial Operations
b. (3x + 4)(–2x + 5) = –6x2
The front terms: –6x2
Example A. Multiply using FOIL method.
a. (x + 3)(x – 4) = x2 – x – 12
The last terms: –12
20. Special Binomial Operations
b. (3x + 4)(–2x + 5) = –6x2
Outer pair: 15x
Example A. Multiply using FOIL method.
a. (x + 3)(x – 4) = x2 – x – 12
The last terms: –12
21. Special Binomial Operations
b. (3x + 4)(–2x + 5) = –6x2
Inner pair: 15x – 8x
Example A. Multiply using FOIL method.
a. (x + 3)(x – 4) = x2 – x – 12
The last terms: –12
22. Special Binomial Operations
b. (3x + 4)(–2x + 5) = –6x2 + 7x
Outer and Inner pair: 15x – 8x = 7x
Example A. Multiply using FOIL method.
a. (x + 3)(x – 4) = x2 – x – 12
The last terms: –12
23. Special Binomial Operations
b. (3x + 4)(–2x + 5) = –6x2 + 7x + 20
Example A. Multiply using FOIL method.
a. (x + 3)(x – 4) = x2 – x – 12
The last terms: 20
The last terms: –12
24. Special Binomial Operations
b. (3x + 4)(–2x + 5) = –6x2 + 7x + 20
Example A. Multiply using FOIL method.
a. (x + 3)(x – 4) = x2 – x – 12
The last terms: 20
The last terms: –12
Expanding the negative of the binomial product requires
extra care.
25. Special Binomial Operations
b. (3x + 4)(–2x + 5) = –6x2 + 7x + 20
Example A. Multiply using FOIL method.
a. (x + 3)(x – 4) = x2 – x – 12
The last terms: 20
The last terms: –12
Expanding the negative of the binomial product requires
extra care. One way to do this is to insert a set of “[ ]”
around the product.
26. Special Binomial Operations
b. (3x + 4)(–2x + 5) = –6x2 + 7x + 20
Example A. Multiply using FOIL method.
a. (x + 3)(x – 4) = x2 – x – 12
The last terms: 20
The last terms: –12
Expanding the negative of the binomial product requires
extra care. One way to do this is to insert a set of “[ ]”
around the product.
Example B. Expand.
a. – (3x – 4)(x + 5)
27. Special Binomial Operations
b. (3x + 4)(–2x + 5) = –6x2 + 7x + 20
Example A. Multiply using FOIL method.
a. (x + 3)(x – 4) = x2 – x – 12
The last terms: 20
The last terms: –12
Expanding the negative of the binomial product requires
extra care. One way to do this is to insert a set of “[ ]”
around the product.
Example B. Expand.
a. – [(3x – 4)(x + 5)] Insert [ ]
28. Special Binomial Operations
b. (3x + 4)(–2x + 5) = –6x2 + 7x + 20
Example A. Multiply using FOIL method.
a. (x + 3)(x – 4) = x2 – x – 12
The last terms: 20
The last terms: –12
Expanding the negative of the binomial product requires
extra care. One way to do this is to insert a set of “[ ]”
around the product.
Example B. Expand.
a. – [(3x – 4)(x + 5)]
= – [ 3x2 + 15x – 4x – 20]
Insert [ ]
Expand
29. Special Binomial Operations
b. (3x + 4)(–2x + 5) = –6x2 + 7x + 20
Example A. Multiply using FOIL method.
a. (x + 3)(x – 4) = x2 – x – 12
The last terms: 20
The last terms: –12
Expanding the negative of the binomial product requires
extra care. One way to do this is to insert a set of “[ ]”
around the product.
Example B. Expand.
a. – [(3x – 4)(x + 5)]
= – [ 3x2 + 15x – 4x – 20]
= – [ 3x2 + 11x – 20]
Insert [ ]
Expand
30. Special Binomial Operations
b. (3x + 4)(–2x + 5) = –6x2 + 7x + 20
Example A. Multiply using FOIL method.
a. (x + 3)(x – 4) = x2 – x – 12
The last terms: 20
The last terms: –12
Expanding the negative of the binomial product requires
extra care. One way to do this is to insert a set of “[ ]”
around the product.
Example B. Expand.
a. – [(3x – 4)(x + 5)]
= – [ 3x2 + 15x – 4x – 20]
= – [ 3x2 + 11x – 20]
= – 3x2 – 11x + 20
Insert [ ]
Expand
Remove [ ] and
change signs.
32. Special Binomial Operations
Another way to do this is to distribute the negative sign into
the first binomial then FOIL.
Example C. Expand.
a. – (3x – 4)(x + 5)
33. Special Binomial Operations
Another way to do this is to distribute the negative sign into
the first binomial then FOIL.
Example C. Expand.
a. – (3x – 4)(x + 5)
= (–3x + 4)(x + 5) Distribute the sign.
34. Special Binomial Operations
Another way to do this is to distribute the negative sign into
the first binomial then FOIL.
Example C. Expand.
a. – (3x – 4)(x + 5)
= (–3x + 4)(x + 5)
= – 3x2 – 15x + 4x + 20
Distribute the sign.
Expand
35. Special Binomial Operations
Another way to do this is to distribute the negative sign into
the first binomial then FOIL.
Example C. Expand.
a. – (3x – 4)(x + 5)
= (–3x + 4)(x + 5)
= – 3x2 – 15x + 4x + 20
= – 3x2 – 11x + 20
Distribute the sign.
Expand
36. Special Binomial Operations
Another way to do this is to distribute the negative sign into
the first binomial then FOIL.
Example C. Expand.
a. – (3x – 4)(x + 5)
= (–3x + 4)(x + 5)
= – 3x2 – 15x + 4x + 20
= – 3x2 – 11x + 20
Distribute the sign.
Expand
b. Expand and simplify. (Two versions)
(2x – 5)(x +3) – (3x – 4)(x + 5)
37. Special Binomial Operations
Another way to do this is to distribute the negative sign into
the first binomial then FOIL.
Example C. Expand.
a. – (3x – 4)(x + 5)
= (–3x + 4)(x + 5)
= – 3x2 – 15x + 4x + 20
= – 3x2 – 11x + 20
Distribute the sign.
Expand
b. Expand and simplify. (Two versions)
(2x – 5)(x +3) – (3x – 4)(x + 5)
= (2x – 5)(x +3) + (–3x + 4)(x + 5)
38. Special Binomial Operations
Another way to do this is to distribute the negative sign into
the first binomial then FOIL.
Example C. Expand.
a. – (3x – 4)(x + 5)
= (–3x + 4)(x + 5)
= – 3x2 – 15x + 4x + 20
= – 3x2 – 11x + 20
Distribute the sign.
Expand
b. Expand and simplify. (Two versions)
(2x – 5)(x +3) – (3x – 4)(x + 5)
= (2x – 5)(x +3) + (–3x + 4)(x + 5)
= 2x2 + 6x – 5x – 15 + (–3x2 –15x + 4x + 20)
39. Special Binomial Operations
Another way to do this is to distribute the negative sign into
the first binomial then FOIL.
Example C. Expand.
a. – (3x – 4)(x + 5)
= (–3x + 4)(x + 5)
= – 3x2 – 15x + 4x + 20
= – 3x2 – 11x + 20
Distribute the sign.
Expand
b. Expand and simplify. (Two versions)
(2x – 5)(x +3) – (3x – 4)(x + 5)
= (2x – 5)(x +3) + (–3x + 4)(x + 5)
= 2x2 + 6x – 5x – 15 + (–3x2 –15x + 4x + 20)
= 2x2 + x – 15 – 3x2 – 11x + 20
40. Special Binomial Operations
Another way to do this is to distribute the negative sign into
the first binomial then FOIL.
Example C. Expand.
a. – (3x – 4)(x + 5)
= (–3x + 4)(x + 5)
= – 3x2 – 15x + 4x + 20
= – 3x2 – 11x + 20
Distribute the sign.
Expand
b. Expand and simplify. (Two versions)
(2x – 5)(x +3) – (3x – 4)(x + 5)
= (2x – 5)(x +3) + (–3x + 4)(x + 5)
= 2x2 + 6x – 5x – 15 + (–3x2 –15x + 4x + 20)
= 2x2 + x – 15 – 3x2 – 11x + 20
= –x2 – 10x + 5
41. Special Binomial Operations
Another way to do this is to distribute the negative sign into
the first binomial then FOIL.
Example C. Expand.
a. – (3x – 4)(x + 5)
= (–3x + 4)(x + 5)
= – 3x2 – 15x + 4x + 20
= – 3x2 – 11x + 20
Distribute the sign.
Expand
b. Expand and simplify. (Two versions)
(2x – 5)(x +3) – (3x – 4)(x + 5)
= (2x – 5)(x +3) + (–3x + 4)(x + 5)
= 2x2 + 6x – 5x – 15 + (–3x2 –15x + 4x + 20)
= 2x2 + x – 15 – 3x2 – 11x + 20
= –x2 – 10x + 5
(2x – 5)(x +3) – (3x – 4)(x + 5)
42. Special Binomial Operations
Another way to do this is to distribute the negative sign into
the first binomial then FOIL.
Example C. Expand.
a. – (3x – 4)(x + 5)
= (–3x + 4)(x + 5)
= – 3x2 – 15x + 4x + 20
= – 3x2 – 11x + 20
Distribute the sign.
Expand
b. Expand and simplify. (Two versions)
(2x – 5)(x +3) – (3x – 4)(x + 5)
= (2x – 5)(x +3) + (–3x + 4)(x + 5)
= 2x2 + 6x – 5x – 15 + (–3x2 –15x + 4x + 20)
= 2x2 + x – 15 – 3x2 – 11x + 20
= –x2 – 10x + 5
(2x – 5)(x +3) – [(3x – 4)(x + 5)] Insert brackets
43. Special Binomial Operations
Another way to do this is to distribute the negative sign into
the first binomial then FOIL.
Example C. Expand.
a. – (3x – 4)(x + 5)
= (–3x + 4)(x + 5)
= – 3x2 – 15x + 4x + 20
= – 3x2 – 11x + 20
Distribute the sign.
Expand
b. Expand and simplify. (Two versions)
(2x – 5)(x +3) – (3x – 4)(x + 5)
= (2x – 5)(x +3) + (–3x + 4)(x + 5)
= 2x2 + 6x – 5x – 15 + (–3x2 –15x + 4x + 20)
= 2x2 + x – 15 – 3x2 – 11x + 20
= –x2 – 10x + 5
(2x – 5)(x +3) – [(3x – 4)(x + 5)]
= 2x2 + x – 15 – [3x2 +11x – 20]
Insert brackets
Expand
44. Special Binomial Operations
Another way to do this is to distribute the negative sign into
the first binomial then FOIL.
Example C. Expand.
a. – (3x – 4)(x + 5)
= (–3x + 4)(x + 5)
= – 3x2 – 15x + 4x + 20
= – 3x2 – 11x + 20
Distribute the sign.
Expand
b. Expand and simplify. (Two versions)
(2x – 5)(x +3) – (3x – 4)(x + 5)
= (2x – 5)(x +3) + (–3x + 4)(x + 5)
= 2x2 + 6x – 5x – 15 + (–3x2 –15x + 4x + 20)
= 2x2 + x – 15 – 3x2 – 11x + 20
= –x2 – 10x + 5
(2x – 5)(x +3) – [(3x – 4)(x + 5)] Insert brackets
= 2x2 + x – 15 – [3x2 +11x – 20]
= 2x2 + x – 15 – 3x2 – 11x + 20
= –x2 – 10x + 5
Expand
Remove brackets
and combine
45. Special Binomial Operations
Another way to do this is to distribute the negative sign into
the first binomial then FOIL.
Example C. Expand.
a. – (3x – 4)(x + 5)
= (–3x + 4)(x + 5)
= – 3x2 – 15x + 4x + 20
= – 3x2 – 11x + 20
Distribute the sign.
Expand
b. Expand and simplify. (Two versions)
(2x – 5)(x +3) – (3x – 4)(x + 5)
= (2x – 5)(x +3) + (–3x + 4)(x + 5)
= 2x2 + 6x – 5x – 15 + (–3x2 –15x + 4x + 20)
= 2x2 + x – 15 – 3x2 – 11x + 20
= –x2 – 10x + 5
(2x – 5)(x +3) – [(3x – 4)(x + 5)] Insert brackets
= 2x2 + x – 15 – [3x2 +11x – 20]
= 2x2 + x – 15 – 3x2 – 11x + 20
= –x2 – 10x + 5
Expand
Remove brackets
and combine
47. Special Binomial Operations
If the binomials are in x and y, then the products consist of
the x2, xy and y2 terms. That is,
(#x + #y)(#x + #y) = #x2 + #xy + #y2
48. Special Binomial Operations
If the binomials are in x and y, then the products consist of
the x2, xy and y2 terms. That is,
(#x + #y)(#x + #y) = #x2 + #xy + #y2
The FOIL method is still applicable in this case.
49. Special Binomial Operations
If the binomials are in x and y, then the products consist of
the x2, xy and y2 terms. That is,
Example D. Expand.
(3x – 4y)(x + 5y)
(#x + #y)(#x + #y) = #x2 + #xy + #y2
The FOIL method is still applicable in this case.
50. Special Binomial Operations
If the binomials are in x and y, then the products consist of
the x2, xy and y2 terms. That is,
Example D. Expand.
(3x – 4y)(x + 5y)
= 3x2
(#x + #y)(#x + #y) = #x2 + #xy + #y2
The FOIL method is still applicable in this case.
F
51. Special Binomial Operations
If the binomials are in x and y, then the products consist of
the x2, xy and y2 terms. That is,
Example D. Expand.
(3x – 4y)(x + 5y)
= 3x2 + 15xy – 4yx
(#x + #y)(#x + #y) = #x2 + #xy + #y2
The FOIL method is still applicable in this case.
F OI
52. Special Binomial Operations
If the binomials are in x and y, then the products consist of
the x2, xy and y2 terms. That is,
Example D. Expand.
(3x – 4y)(x + 5y)
= 3x2 + 15xy – 4yx – 20y2
(#x + #y)(#x + #y) = #x2 + #xy + #y2
The FOIL method is still applicable in this case.
F OI L
53. Special Binomial Operations
If the binomials are in x and y, then the products consist of
the x2, xy and y2 terms. That is,
Example D. Expand.
(3x – 4y)(x + 5y)
= 3x2 + 15xy – 4yx – 20y2
= 3x2 + 11xy – 20y2
(#x + #y)(#x + #y) = #x2 + #xy + #y2
The FOIL method is still applicable in this case.
55. There are some important patterns in multiplying expressions
that it is worthwhile to memorize.
Multiplication Formulas
56. The two binomials (A + B) and (A – B) are said to be the
conjugate of each other.
There are some important patterns in multiplying expressions
that it is worthwhile to memorize.
Multiplication Formulas
57. The two binomials (A + B) and (A – B) are said to be the
conjugate of each other.
For example, the conjugate of (3x + 2) is (3x – 2),
There are some important patterns in multiplying expressions
that it is worthwhile to memorize.
Multiplication Formulas
58. The two binomials (A + B) and (A – B) are said to be the
conjugate of each other.
For example, the conjugate of (3x + 2) is (3x – 2), and
the conjugate of (2ab – c) is (2ab + c).
There are some important patterns in multiplying expressions
that it is worthwhile to memorize.
Multiplication Formulas
59. The two binomials (A + B) and (A – B) are said to be the
conjugate of each other.
For example, the conjugate of (3x + 2) is (3x – 2), and
the conjugate of (2ab – c) is (2ab + c).
Note: The conjugate is different from the opposite.
The opposite of (3x + 2) is (–3x – 2).
There are some important patterns in multiplying expressions
that it is worthwhile to memorize.
Multiplication Formulas
60. The two binomials (A + B) and (A – B) are said to be the
conjugate of each other.
There are some important patterns in multiplying expressions
that it is worthwhile to memorize.
I. Difference of Squares Formula
Multiplication Formulas
For example, the conjugate of (3x + 2) is (3x – 2), and
the conjugate of (2ab – c) is (2ab + c).
Note: The conjugate is different from the opposite.
The opposite of (3x + 2) is (–3x – 2).
61. The two binomials (A + B) and (A – B) are said to be the
conjugate of each other.
There are some important patterns in multiplying expressions
that it is worthwhile to memorize.
I. Difference of Squares Formula
(A + B)(A – B)
Conjugate Product
Multiplication Formulas
For example, the conjugate of (3x + 2) is (3x – 2), and
the conjugate of (2ab – c) is (2ab + c).
Note: The conjugate is different from the opposite.
The opposite of (3x + 2) is (–3x – 2).
62. The two binomials (A + B) and (A – B) are said to be the
conjugate of each other.
There are some important patterns in multiplying expressions
that it is worthwhile to memorize.
I. Difference of Squares Formula
(A + B)(A – B) = A2 – B2
Conjugate Product Difference of Squares
Multiplication Formulas
For example, the conjugate of (3x + 2) is (3x – 2), and
the conjugate of (2ab – c) is (2ab + c).
Note: The conjugate is different from the opposite.
The opposite of (3x + 2) is (–3x – 2).
63. The two binomials (A + B) and (A – B) are said to be the
conjugate of each other.
There are some important patterns in multiplying expressions
that it is worthwhile to memorize.
I. Difference of Squares Formula
(A + B)(A – B) = A2 – B2
To verify this :
(A + B)(A – B)
Conjugate Product Difference of Squares
Multiplication Formulas
For example, the conjugate of (3x + 2) is (3x – 2), and
the conjugate of (2ab – c) is (2ab + c).
Note: The conjugate is different from the opposite.
The opposite of (3x + 2) is (–3x – 2).
64. The two binomials (A + B) and (A – B) are said to be the
conjugate of each other.
There are some important patterns in multiplying expressions
that it is worthwhile to memorize.
I. Difference of Squares Formula
(A + B)(A – B) = A2 – B2
To verify this :
(A + B)(A – B) = A2 – AB + AB – B2
Conjugate Product Difference of Squares
Multiplication Formulas
For example, the conjugate of (3x + 2) is (3x – 2), and
the conjugate of (2ab – c) is (2ab + c).
Note: The conjugate is different from the opposite.
The opposite of (3x + 2) is (–3x – 2).
65. The two binomials (A + B) and (A – B) are said to be the
conjugate of each other.
There are some important patterns in multiplying expressions
that it is worthwhile to memorize.
I. Difference of Squares Formula
(A + B)(A – B) = A2 – B2
To verify this :
(A + B)(A – B) = A2 – AB + AB – B2
= A2 – B2
Conjugate Product Difference of Squares
Multiplication Formulas
For example, the conjugate of (3x + 2) is (3x – 2), and
the conjugate of (2ab – c) is (2ab + c).
Note: The conjugate is different from the opposite.
The opposite of (3x + 2) is (–3x – 2).
73. Multiplication Formulas
Example D. Expand.
a. (3x + 2)(3x – 2)
Here are some examples of squaring: (3x)2 = 9x2,
(2xy)2 = 4x2y2, and (5z2)2 = 25z4.
74. Multiplication Formulas
Example D. Expand.
a. (3x + 2)(3x – 2)
(A + B)(A – B)
Here are some examples of squaring: (3x)2 = 9x2,
(2xy)2 = 4x2y2, and (5z2)2 = 25z4.
75. Multiplication Formulas
Example D. Expand.
a. (3x + 2)(3x – 2) = (3x)2 – (2)2
(A + B)(A – B) = A2 – B2
Here are some examples of squaring: (3x)2 = 9x2,
(2xy)2 = 4x2y2, and (5z2)2 = 25z4.
76. Multiplication Formulas
Example D. Expand.
a. (3x + 2)(3x – 2) = (3x)2 – (2)2 = 9x2 – 4
(A + B)(A – B) = A2 – B2
Here are some examples of squaring: (3x)2 = 9x2,
(2xy)2 = 4x2y2, and (5z2)2 = 25z4.
77. Multiplication Formulas
Example D. Expand.
a. (3x + 2)(3x – 2) = (3x)2 – (2)2 = 9x2 – 4
(A + B)(A – B) = A2 – B2
b. (2xy – 5z2)(2xy + 5z2)
Here are some examples of squaring: (3x)2 = 9x2,
(2xy)2 = 4x2y2, and (5z2)2 = 25z4.
78. Multiplication Formulas
Example D. Expand.
a. (3x + 2)(3x – 2) = (3x)2 – (2)2 = 9x2 – 4
(A + B)(A – B) = A2 – B2
b. (2xy – 5z2)(2xy + 5z2)
= (2xy)2 – (5z2)2
Here are some examples of squaring: (3x)2 = 9x2,
(2xy)2 = 4x2y2, and (5z2)2 = 25z4.
79. Multiplication Formulas
Example D. Expand.
a. (3x + 2)(3x – 2) = (3x)2 – (2)2 = 9x2 – 4
(A + B)(A – B) = A2 – B2
b. (2xy – 5z2)(2xy + 5z2)
= (2xy)2 – (5z2)2
= 4x2y2 – 25z4
Here are some examples of squaring: (3x)2 = 9x2,
(2xy)2 = 4x2y2, and (5z2)2 = 25z4.
80. Multiplication Formulas
Example D. Expand.
a. (3x + 2)(3x – 2) = (3x)2 – (2)2 = 9x2 – 4
(A + B)(A – B) = A2 – B2
b. (2xy – 5z2)(2xy + 5z2)
= (2xy)2 – (5z2)2
= 4x2y2 – 25z4
Here are some examples of squaring: (3x)2 = 9x2,
(2xy)2 = 4x2y2, and (5z2)2 = 25z4.
II. Square Formulas
81. Multiplication Formulas
Example D. Expand.
a. (3x + 2)(3x – 2) = (3x)2 – (2)2 = 9x2 – 4
(A + B)(A – B) = A2 – B2
b. (2xy – 5z2)(2xy + 5z2)
= (2xy)2 – (5z2)2
= 4x2y2 – 25z4
Here are some examples of squaring: (3x)2 = 9x2,
(2xy)2 = 4x2y2, and (5z2)2 = 25z4.
II. Square Formulas
(A + B)2 = A2 + 2AB + B2
82. Multiplication Formulas
Example D. Expand.
a. (3x + 2)(3x – 2) = (3x)2 – (2)2 = 9x2 – 4
(A + B)(A – B) = A2 – B2
b. (2xy – 5z2)(2xy + 5z2)
= (2xy)2 – (5z2)2
= 4x2y2 – 25z4
Here are some examples of squaring: (3x)2 = 9x2,
(2xy)2 = 4x2y2, and (5z2)2 = 25z4.
II. Square Formulas
(A + B)2 = A2 + 2AB + B2
(A – B)2 = A2 – 2AB + B2
83. Multiplication Formulas
Example D. Expand.
a. (3x + 2)(3x – 2) = (3x)2 – (2)2 = 9x2 – 4
(A + B)(A – B) = A2 – B2
b. (2xy – 5z2)(2xy + 5z2)
= (2xy)2 – (5z2)2
= 4x2y2 – 25z4
Here are some examples of squaring: (3x)2 = 9x2,
(2xy)2 = 4x2y2, and (5z2)2 = 25z4.
II. Square Formulas
(A + B)2 = A2 + 2AB + B2
(A – B)2 = A2 – 2AB + B2
We may check this easily by multiplying,
84. Multiplication Formulas
Example D. Expand.
a. (3x + 2)(3x – 2) = (3x)2 – (2)2 = 9x2 – 4
(A + B)(A – B) = A2 – B2
b. (2xy – 5z2)(2xy + 5z2)
= (2xy)2 – (5z2)2
= 4x2y2 – 25z4
Here are some examples of squaring: (3x)2 = 9x2,
(2xy)2 = 4x2y2, and (5z2)2 = 25z4.
II. Square Formulas
(A + B)2 = A2 + 2AB + B2
(A – B)2 = A2 – 2AB + B2
We may check this easily by multiplying,
(A + B)2 = (A + B)(A + B)
85. Multiplication Formulas
Example D. Expand.
a. (3x + 2)(3x – 2) = (3x)2 – (2)2 = 9x2 – 4
(A + B)(A – B) = A2 – B2
b. (2xy – 5z2)(2xy + 5z2)
= (2xy)2 – (5z2)2
= 4x2y2 – 25z4
Here are some examples of squaring: (3x)2 = 9x2,
(2xy)2 = 4x2y2, and (5z2)2 = 25z4.
II. Square Formulas
(A + B)2 = A2 + 2AB + B2
(A – B)2 = A2 – 2AB + B2
We may check this easily by multiplying,
(A + B)2 = (A + B)(A + B) = A2 + AB + BA + B2
86. Multiplication Formulas
Example D. Expand.
a. (3x + 2)(3x – 2) = (3x)2 – (2)2 = 9x2 – 4
(A + B)(A – B) = A2 – B2
b. (2xy – 5z2)(2xy + 5z2)
= (2xy)2 – (5z2)2
= 4x2y2 – 25z4
Here are some examples of squaring: (3x)2 = 9x2,
(2xy)2 = 4x2y2, and (5z2)2 = 25z4.
II. Square Formulas
(A + B)2 = A2 + 2AB + B2
(A – B)2 = A2 – 2AB + B2
We may check this easily by multiplying,
(A + B)2 = (A + B)(A + B) = A2 + AB + BA + B2 = A2 + 2AB + B2
87. Multiplication Formulas
Example D. Expand.
a. (3x + 2)(3x – 2) = (3x)2 – (2)2 = 9x2 – 4
(A + B)(A – B) = A2 – B2
b. (2xy – 5z2)(2xy + 5z2)
= (2xy)2 – (5z2)2
= 4x2y2 – 25z4
Here are some examples of squaring: (3x)2 = 9x2,
(2xy)2 = 4x2y2, and (5z2)2 = 25z4.
II. Square Formulas
(A + B)2 = A2 + 2AB + B2
(A – B)2 = A2 – 2AB + B2
We may check this easily by multiplying,
(A + B)2 = (A + B)(A + B) = A2 + AB + BA + B2 = A2 + 2AB + B2
We say that “(A + B)2 is A2, B2, plus twice A*B”,
88. Multiplication Formulas
Example D. Expand.
a. (3x + 2)(3x – 2) = (3x)2 – (2)2 = 9x2 – 4
(A + B)(A – B) = A2 – B2
b. (2xy – 5z2)(2xy + 5z2)
= (2xy)2 – (5z2)2
= 4x2y2 – 25z4
Here are some examples of squaring: (3x)2 = 9x2,
(2xy)2 = 4x2y2, and (5z2)2 = 25z4.
II. Square Formulas
(A + B)2 = A2 + 2AB + B2
(A – B)2 = A2 – 2AB + B2
We may check this easily by multiplying,
(A + B)2 = (A + B)(A + B) = A2 + AB + BA + B2 = A2 + 2AB + B2
We say that “(A + B)2 is A2, B2, plus twice A*B”,
and “(A – B)2 is A2, B2, minus twice A*B”.