MULTIPLYING BINOMIALS WORKSHEET

Problem 1 :

Simplify :

(2a + 3b)(5a + 4b)

Problem 2 :

Simplify :

(5 - 2y)(4 + y)

Problem 3 :

Simplify : 

(3 + 2p)(4p - 3)

Problem 4 :

Simplify :

(2m + 3)(m + 5)

Problem 5 :

Simplify :

(3p - 2q)(p + 5q)

Problem 6 :

Simplify :

(5a + 3b)(a - 2b)

Problem 7 :

Simplify : 

(p - 2)(p - 3)

Problem 8 :

Simplify : 

(p² - 3)(p + 4)

Problem 9 :

Simplify : 

(x + 3)(x - 3)

Problem 10 :

Simplify : 

(3x + 5y)(3x - 5y)

Answers

1. Answer :

=  (2a + 3b)(5a + 4b)

=  2a(5a) + 2a(4b) + 3b(5a) + 3b(4b)

=  10a² + 8ab + 15ab + 12b²

Combine the like terms.

=  10a² + 23ab + 12b²

2. Answer :

=  (5 - 2y)(4 + y)

=  5(4) + 5(y) - 2y(4) - 2y(y)

=  20 + 5y - 8y - 2y²

Combine the like terms.

=  20 - 3y - 2y²

3. Answer :

=  (3 + 2p)(4p - 3)

=  3(4p) + 3(-3) + 2p(4p) + 2p(-3)

=  12p - 9 + 8p² - 6p

Combine the like terms.

=  8p² + 6p - 9

4. Answer :

=  (2m + 3)(m + 5)

=  2m(m) + 2m(5) + 3(m) + 3(5)

=  2m² + 10m + 3m + 15

Combine the like terms. 

=  2m² + 13m + 15

5. Answer :

=  (3p - 2q)(p + 5q)

=  3p(p) + 3p(5q) - 2q(p) - 2q(5q)

=  3p² + 15pq - 2pq - 10q²

Combining the like terms

=  3p² + 13pq - 10q²

6. Answer :

=  (5a + 3b)(a - 2b)

=  5a(a) + 5a(-2b) + 3b(a) + 3b(-2b)

=  5a² - 10ab + 3ab - 6b²

Combine the like terms.

=  5a² - 7ab - 6b²

7. Answer :

=  (p - 2)(p - 3)

=  p(p) + p(-3) - 2(p) - 2(-3)

=  p² - 3p - 2p + 6

Combine the like terms.

=  p² - 5p + 6

8. Answer :

=  (p² - 3)(p + 4)

=  p²(p) + p²(4) - 3(p) - 3(4)

=  p³ + 4p² - 3p - 12

9. Answer :

=  (x + 3)(x - 3)

Using the identity, a² - b²  =  (a + b)(a - b),

=  x² - 3²

=  x² - 9

10. Answer :

=  (3x + 5y)(3x - 5y)

Using the identity, a² - b²  =  (a + b)(a - b),

=  (3x)² - (5y)²

=  3²x² - 5²y²

=  9x² - 25y²

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