# FACTORING BINOMIALS WORKSHEET

Problem 1 :

4x + 10

Problem 2 :

5y - 15

Problem 3 :

7p2 + 21p

Problem 4 :

3x + 9xy

Problem 5 :

39pq2 - 52p2q

Problem 6 :

60a2b3 + 75ab6

Problem 7 :

y2 - 25

Problem 8 :

9x2 - 49

Problem 9 :

16a2 - 25b2

Problem 10 :

= 4x + 10

The largest common divisor for 4x and 10 is 2.

Divide 4x and 10 by 2.

Write the quotients 2x and 5 inside the parentheses and multiply by the largest common divisor 2.

= 2(2x + 5)

= 5y - 15

The largest common divisor for 5y and 15 is 5.

Divide 5y and 15 by 5.

Write the quotients y and 3 inside the parentheses and multiply by the largest common divisor 5.

= 7p2 + 21p

The largest common divisor for 7p2 and 21p.

Divide 7p2 and 21p is 7p.

Write the quotients p and 3 inside the parentheses and multiply by the largest common divisor 7p.

= 7p(p + 3)

= 3x + 9xy

The largest common divisor for 3x and 9xy is 3x.

Divide 3x and 9xy is 3x.

L

Write the quotients 1 and 3x inside the parentheses and multiply by the largest common divisor 2y.

= 3x(1 + 2y)

= 39pq2 - 52p2q

The largest common divisor for 39 and 52 is 13.

The largest common divisor for p and p2 is p.

The largest common divisor for q2 and q is q.

Therefore, the largest common divisor of 39pq2 and 52p2is 13pq.

Divide 39pq2 and 52p2q by 13pq.

Write the quotients 3q and 4p inside the parentheses and multiply by the largest common divisor 13pq.

= 13pq(3q + 4p)

= 60a2b3 + 75ab6

The largest common divisor for 60 and 75 is 15.

The largest common divisor for a2 and a is a.

The largest common divisor for b3 and b6 is b3.

Therefore, the largest common divisor of 60a2b3 and 75ab6 is 15ab3.

Divide 60a2a3 and 75ab6 by 15ab3.

Write the quotients 4a and 5b3 inside the parentheses and multiply by the largest common divisor 15ab3.

= 15ab3(4a + 5b3)

The given binomial (y2 - 25) can be written as a difference of two squares. Then, we can factor it using the following algebraic identity.

a2 - a2 = (a + b)(a - b)

= y2 - 25

= y2 - 52

= (y + 5)(y - 5)

= 9x2 - 49

= 32x2 - 72

= (3x)2 - 72

= (3x + 7)(3x - 7)

= 16a2 - 25b2

= 42a2 - 52b2

= (4a)2 - (5b)2

= (4a + 5b)(4a - 5b)

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