1. Cancellation (of Factors)

2. Any mathematics expression is the addition or subtractions of
one or more quantities.
Cancellation (of Factors)

3. Any mathematics expression is the addition or subtractions of
one or more quantities. These quantities are called terms.
Cancellation (of Factors)

4. Any mathematics expression is the addition or subtractions of
one or more quantities. These quantities are called terms.
Example A.
a. 3xy + 2x – yz has three terms
Cancellation (of Factors)

5. Any mathematics expression is the addition or subtractions of
one or more quantities. These quantities are called terms.
Example A.
a. 3xy + 2x – yz has three terms; 3xy, 2x and yz.
Cancellation (of Factors)

6. Any mathematics expression is the addition or subtractions of
one or more quantities. These quantities are called terms.
Example A.
a. 3xy + 2x – yz has three terms; 3xy, 2x and yz.
b. x(y + z) is one term,
Cancellation (of Factors)

7. Any mathematics expression is the addition or subtractions of
one or more quantities. These quantities are called terms.
Example A.
a. 3xy + 2x – yz has three terms; 3xy, 2x and yz.
b. x(y + z) is one term, but it's expanded form xy + xz has two
terms, xy and xz.
Cancellation (of Factors)

8. Any mathematics expression is the addition or subtractions of
one or more quantities. These quantities are called terms.
Example A.
a. 3xy + 2x – yz has three terms; 3xy, 2x and yz.
b. x(y + z) is one term, but it's expanded form xy + xz has two
terms, xy and xz.
A quantity that is multiplied to other quantities is called a
factor.
Cancellation (of Factors)

9. Any mathematics expression is the addition or subtractions of
one or more quantities. These quantities are called terms.
Example A.
a. 3xy + 2x – yz has three terms; 3xy, 2x and yz.
b. x(y + z) is one term, but it's expanded form xy + xz has two
terms, xy and xz.
A quantity that is multiplied to other quantities is called a
factor.
Example B.
a. 3x2yz has many factors
Cancellation (of Factors)

10. Any mathematics expression is the addition or subtractions of
one or more quantities. These quantities are called terms.
Example A.
a. 3xy + 2x – yz has three terms; 3xy, 2x and yz.
b. x(y + z) is one term, but it's expanded form xy + xz has two
terms, xy and xz.
A quantity that is multiplied to other quantities is called a
factor.
Example B.
a. 3x2yz has many factors; 3,
Cancellation (of Factors)

11. Any mathematics expression is the addition or subtractions of
one or more quantities. These quantities are called terms.
Example A.
a. 3xy + 2x – yz has three terms; 3xy, 2x and yz.
b. x(y + z) is one term, but it's expanded form xy + xz has two
terms, xy and xz.
A quantity that is multiplied to other quantities is called a
factor.
Example B.
a. 3x2yz has many factors; 3, x, y,
Cancellation (of Factors)

12. Any mathematics expression is the addition or subtractions of
one or more quantities. These quantities are called terms.
Example A.
a. 3xy + 2x – yz has three terms; 3xy, 2x and yz.
b. x(y + z) is one term, but it's expanded form xy + xz has two
terms, xy and xz.
A quantity that is multiplied to other quantities is called a
factor.
Example B.
a. 3x2yz has many factors; 3, x, y, yz, x2, yx2, but it's one term.
Cancellation (of Factors)

13. Any mathematics expression is the addition or subtractions of
one or more quantities. These quantities are called terms.
Example A.
a. 3xy + 2x – yz has three terms; 3xy, 2x and yz.
b. x(y + z) is one term, but it's expanded form xy + xz has two
terms, xy and xz.
A quantity that is multiplied to other quantities is called a
factor.
Example B.
a. 3x2yz has many factors; 3, x, y, yz, x2, yx2, but it's one term.
b. x(y + z) has two factors, x and (y + z).
Cancellation (of Factors)

14. Any mathematics expression is the addition or subtractions of
one or more quantities. These quantities are called terms.
Example A.
a. 3xy + 2x – yz has three terms; 3xy, 2x and yz.
b. x(y + z) is one term, but it's expanded form xy + xz has two
terms, xy and xz.
A quantity that is multiplied to other quantities is called a
factor.
P
Q
Given a fraction , common factor of P and Q may
be canceled. Terms may not be canceled.
Example B.
a. 3x2yz has many factors; 3, x, y, yz, x2, yx2, but it's one term.
b. x(y + z) has two factors, x and (y + z).
Cancellation (of Factors)

15. Cancellation (of Factors)
Any mathematics expression is the addition or subtractions of
one or more quantities. These quantities are called terms.
Example A.
a. 3xy + 2x – yz has three terms; 3xy, 2x and yz.
b. x(y + z) is one term, but it's expanded form xy + xz has two
terms, xy and xz.
A quantity that is multiplied to other quantities is called a
factor.
P
Q
Given a fraction , common factor of P and Q may
be canceled. Terms may not be canceled.
In other words, in order to simplify a fraction, the fraction
must be in the factored form.
Example B.
a. 3x2yz has many factors; 3, x, y, yz, x2, yx2, but it's one term.
b. x(y + z) has two factors, x and (y + z).

16. 4
6
=
2*2
2*3
Example C.
a.
Cancellation (of Factors)

17. 4
6
=
2*2
2*3
Example C.
a.
Cancellation (of Factors)

18. 4
6
=
2*2
2*3
=
2
3
Example C.
a.
Cancellation (of Factors)

19. 4
6
=
2*2
2*3
=
2
3
4
6
=
3 + 1
3 + 3
Example C.
a.
Cancellation (of Factors)

20. 4
6
=
2*2
2*3
=
2
3
4
6
=
3 + 1
3 + 3 =
3 + 1
3 + 3
Example C.
a.
Cancellation (of Factors)

21. 4
6
=
2*2
2*3
=
2
3
4
6
=
3 + 1
3 + 3 =
3 + 1
3 + 3
Example C.
a.
x2y
xz =
xxy
xz
b.
Cancellation (of Factors)

22. 4
6
=
2*2
2*3
=
2
3
4
6
=
3 + 1
3 + 3 =
3 + 1
3 + 3
Example C.
a.
x2y
xz =
xxy
xz =
xy
z ,
b.
Cancellation (of Factors)

23. 4
6
=
2*2
2*3
=
2
3
4
6
=
3 + 1
3 + 3 =
3 + 1
3 + 3
Example C.
a.
x2y
xz =
xxy
xz =
xy
z ,
x2 + y
xz , no cancellation!b.
Cancellation (of Factors)

24. 4
6
=
2*2
2*3
=
2
3
4
6
=
3 + 1
3 + 3 =
3 + 1
3 + 3
Example C.
a.
x2y
xz =
xxy
xz =
xy
z ,
x2 + y
xz , no cancellation!b.
(x + y)(2x – y)
(2x +y) (x + y)
c.
Cancellation (of Factors)

25. 4
6
=
2*2
2*3
=
2
3
4
6
=
3 + 1
3 + 3 =
3 + 1
3 + 3
Example C.
a.
x2y
xz =
xxy
xz =
xy
z ,
x2 + y
xz , no cancellation!b.
(x + y)(2x – y)
(2x +y) (x + y)
=
2x – y
2x + y ,
c.
Cancellation (of Factors)

26. 4
6
=
2*2
2*3
=
2
3
4
6
=
3 + 1
3 + 3 =
3 + 1
3 + 3
Example C.
a.
x2y
xz =
xxy
xz =
xy
z ,
x2 + y
xz , no cancellation!b.
(x + y)(2x – y)
(2x +y) (x + y)
=
2x – y
2x + y ,
(x + y) + (2x – y)
(2x + y)+ (x + y)
c.
Cancellation (of Factors)

27. 4
6
=
2*2
2*3
=
2
3
4
6
=
3 + 1
3 + 3 =
3 + 1
3 + 3
Example C.
a.
x2y
xz =
xxy
xz =
xy
z ,
x2 + y
xz , no cancellation!b.
(x + y)(2x – y)
(2x +y) (x + y)
=
2x – y
2x + y ,
(x + y) + (2x – y)
(2x + y) + (x + y)
c.
No cancellation!
Cancellation (of Factors)

28. 4
6
=
2*2
2*3
=
2
3
4
6
=
3 + 1
3 + 3 =
3 + 1
3 + 3
Example C.
a.
x2y
xz =
xxy
xz =
xy
z ,
x2 + y
xz , no cancellation!b.
(x + y)(2x – y)
(2x +y) (x + y)
=
2x – y
2x + y ,
(x + y) + (2x – y)
(2x + y) + (x + y) =
3x
3x + 2y
c.
No cancellation!
Cancellation (of Factors)

29. 4
6
=
2*2
2*3
=
2
3
4
6
=
3 + 1
3 + 3 =
3 + 1
3 + 3
Example C.
a.
x2y
xz =
xxy
xz =
xy
z ,
x2 + y
xz , no cancellation!b.
(x + y)(2x – y)
(2x +y) (x + y)
=
2x – y
2x + y ,
(x + y) + (2x – y)
(2x + y) + (x + y) =
3x
3x + 2y
c.
No cancellation!
Cancellation (of Factors)
All of them are terms!
The ( )’s don’t serve any operational purposes.

30. 3(5)
3
3 + 5
3
Ex. Determine if the each of the following expressions is in
the factored form. If not, write it in the factored form then
reduce the expression by cancellation, if possible.
1. 2. xy
x
x + y
x3. 4.
5. 8.xy + y
y
x + yx
xy – y6. 7.
y – x
x – y9.
(x + y) (x – y)
(y – x) (x + y)
10.
(x + y) + (x – y)
(y – x) (x + y)11.
(x + y)z + (x + y)z
(y – x)(x + y)12.
x(x + 2) + 2(x + 2)
x (x + 2)
13.
x(x + 1) + 6(x + 2)
x (x + 2)
14.
(x – 3)(x – 3) – (x + 2)(x + 2)
(x – 3) (x + 2)
15.
3(5) + 7
3
x2 + y2
xy
Cancellation (of Factors)