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 :

Answers

1. Answer :

= 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)

2. Answer :

= 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.

3. Answer :

= 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)

4. Answer :

= 3x + 9xy

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

Divide 3x and 9xy is 3x.

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

= 3x(1 + 2y)

5. Answer :

= 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 52p²q is 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)

6. Answer :

= 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)

7. Answer :

= y² - 25

= y² - 5²

= (y + 5)(y - 5)

8. Answer :

= 9x² - 49

= 3²x² - 7²

= (3x)² - 7²

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

9. Answer :

= 16a² - 25b²

= 4²a² - 5²b²

= (4a)² - (5b)²

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

10. Answer :

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