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Multiplication of polynomials
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The process of multiplying polynomials.
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Multiplication of polynomials
1.
Multiplication of Polynomials
2.
1. -t4 +
5t3 + 3t2 - 16 Answer to the assignment: 2. 5x + 2y - 6
3.
Review: Multiply the following
monomials: (3)(4x) = 12x (5x3 y2)(2x3y) = (y3)(-y3) = (3x2)(4xy3) = (6xy4)(2x3y3) = (-x4y3)(-x3y3) = (2xy5)(-8x3y) = (7xy4)(2x3y3) = 10x6y3 -y6 12x3y3 12x4y7 x7y6 -16x4y6 14x4y7
4.
Combine like terms
(if you can). Distribute each term of the first polynomial to every term of the second polynomial. Remember that when you multiply two terms together you must multiply the coefficient (numbers) and add the exponents.
5.
Multiply: 1. 3x2(4x2 –
5x + 7) 12x4 – 15x3 + 21x2 2. 6v(2v + 3) 12v2 + 18v
6.
3. –6xy(4x2 –
5xy – 2y2) -24x2y + 30x2y2 + 12xy3 4. (3x – 4y)(5x – 2y) 15x2 – 6xy - 20xy + 8y2 15x2 – 26xy + 8y2 +
7.
5. (x −
3)(6x − 2) 6x2 − 2x − 18x + 6 + 6x2 − 20x + 6 6. (8x − 2)(6x + 2) 48x2 + 16x + − 12x - 4 48x2 + 4x - 4
8.
7. (4x –
5)(2x2 + 3x – 6) 8x3 + 12x2 - 24x - 10x2 - 15x + 30 + 8x3 + 2x2 - 39x + 30
9.
8. (3x +
2)(4x2 – 7x + 5) 12x3 – 21x2 + 15x 8x2 – 14x + 10 + 12x3 – 13x2 + x + 10
10.
9. (x2 −
7x − 6)(7x2 − 3x − 7) 7x4 − 3x3 − 7x2 − 49x3 + 21x2 + 49x − 42x2 + 18x + 42 + 7x4 − 52x3 − 28x2 + 67x + 42
11.
Special Products: Sum and
Difference of Two Binomials 1. (x + 5)(x − 5) 1. x2 - 25 (a)2 – (b) 2 2. (x - 8)(x + 8) 2. x2 - 64 3. (x – 2y)(x + 2y) 3. x2 – 4y2 (a – b)(a+b) =
12.
Squares of Two
Binomials (a+b)2 = (a + b)(a + b) = (a)2 ± 2(a)(b) +(b)2 1. (x − 1)2 = (x)2 ± 2(x)(1) +(1)2 = x2 + 2x + 1 2. (x − 6)(x – 6)2 = (x − 6)2 = (x)2 - 2(x)(6) +(6)2 = x2 - 12x + 36 3. (2x − 5)2 = (2x)2 - 2(2x)(5) +(5)2 = 4x2 - 20x + 25
13.
Cube of a
Binomial: (a+b)3 = (a + b)(a + b)(a + b) = (a)3 ± 3(a) 2(b) ± 3(a)(b)2 ± (b) 3 1. (x + 3)3 = (x)3 + 3(x) 2(3) + 3(x)(3)2 + (3) 3 = x3 + 9x 2 + 27x + 27
14.
2. (2x -
5)3 = (2x)3 - 3(2x) 2(5) + 3(2x)(5)2 - (5) 3 = 8x3 - 60x2 + 150x - 125
15.
2. (3x +
7)3 = (3x)3 + 3(3x) 2(7) + 3(3x)(7)2 + (7) 3 = 27x3 + 189x2 + 441x + 343
16.
Find the product: 1.
5x2y(7x2 – 4xy2 + 2y3) 2. (4x – 7)(2x – 9) 3. (4x + 3)(7x – 5) 4. (2x2 – 5x)(9x2 + 6x + 4) 5. (6x2 − 4x − 5)(7x3 + 5x − 5)
17.
6. (x −
3)(x + 3) 7. (2x + 3)2 8. (8a2 + 4)(8a2 − 4) 9. (3x − 7)(3x + 7) 10. (2x − 7)3
18.
Answers: 1. 35x4y -
20x3y3 + 10x2y4 5. 42x5 − 28x4 − 5x3 – 50x2 – 5x + 25 2. 8x2 - 50x + 63 3. 28x2 + x - 15 4. 18x4 - 33x3 + 38x2 - 20x
19.
6. x2 -
9 7. 4x2 + 24x + 9 8. 64x4 - 16 9. 9x2 - 49 10. 8x3 - 84x2 + 294x - 373
20.
Assignment: 1. The dimensions
of a window are 3x + 10 and 2x + 6. What is the area of the window? (assuming the window is rectangle)
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