MULTIPLYING A BINOMIAL BY A BINOMIAL WORKSHEET

Problem 1-4: Multiply using Distributive Property.

Problem 1 :

(x + 3)(x - 6)

Problem 2 : 

(a + b)²

Problem 3 :

(x + 2)²

Problem 4 :

(3a² - b)(a² - 2b)

Problems 5-8 :Multiply using the FOIL method.

Problem 5 : 

(a - b)²

Problem 6 :

(p - 5)²

Problem 7 :

(3b² - c)(b² - 2c)

Problem 8 :

(2x - y²)(x + 4y²)

Answers

1. Answer :

=  (x + 3)(x - 6)

Distribute. 

=  x(x - 6) + 3(x - 6)

Distribute again. 

=  x(x) + x(-6) + 3(x) + 3(-6)

Multiply. 

=  x² - 6x + 3x - 18

Combine like terms. 

=  x² - 3x - 18

2. Answer :

=  (a + b)²

Write as a product of two binomials. 

=  (a + b)(a + b)

Distribute. 

=  a(a + b) + b(a + b)

Distribute again. 

=  a(a) + a(b) + b(a) + b(b)

Multiply. 

=  a² + ab + ab + b²

Combine like terms. 

=  a² + 2ab + b²

3. Answer :

=  (x + 2)²

Write as a product of two binomials. 

=  (x + 2)(x + 2)

Distribute. 

=  x(x + 2) + 2(x + 2)

Distribute again. 

=  x(x) + x(2) + 2(x) + 2(2)

Multiply. 

=  x² + 2x + 2x + 4

Combine like terms. 

=  x² + 4x + 4

4. Answer :

=  (3a² - b)(a² - 2b)

Distribute. 

=  3a²(a² - 2b) - b(a² - 2b)

Distribute again. 

=  3a²(a²) + 3a²(-2b) - b(a²) - b(-2b)

Multiply. 

=  3a⁴ - 6a²b - a²b + 2b²

Combine like terms. 

=  3a⁴ - 7a²b + 2b²

5. Answer :

=  (a - b)²

Write as a product of two binomials. 

=  (a - b)(a - b)

Use the FOIL method. 

=  (a ⋅ a) + (a ⋅ -b) + (-b ⋅ a) + (-b ⋅ -b)

Multiply. 

=  a² - ab - ab + b²

Combine like terms. 

=  a² - 2ab + b²

6. Answer :

=  (p - 5)²

Write as a product of two binomials. 

=  (p - 5)(p - 5)

Use the FOIL method. 

=  (p ⋅ p) + (p ⋅ -5) + (-5 ⋅ p) + (-5 ⋅ -5)

Multiply. 

=  p² - 5p - 5p + 25

Combine like terms. 

=  p² - 10p + 25

7. Answer :

=  (3b² - c)(b² - 2c)

Use the FOIL method. 

=  (3b² ⋅ b²) + (3b²⋅ -2c) + (-c ⋅ b²) + (-c ⋅ -2c)

Multiply. 

=  3b⁴ - 6b²c - b²c + 2c²

Combine like terms. 

=  3b⁴ - 7b²c + 2c²

8. Answer :

=  (2x - y²)(x + 4y²)

Use the FOIL method. 

=  (2x ⋅ x) + (2x ⋅ 4y²) + (-y² ⋅ x) + (-y² ⋅ 4y²)

Multiply. 

=  2x² + 8xy² - xy² - 4y⁴

Combine like terms. 

=  2x² - 7xy² - 4y⁴

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