WORKSHEET ON MULTIPLYING POLYNOMIALS

Multiply : 

1)  (4x²)(5x³)

2)  (a²b²c³)(abc²)

3)  (0.5a³b)(a²c²)(6b²)

4)  2(3x² + 5x + 7)

5)  3ab(5a² + b)

6)  2xy(x²y + xz - xy)

Multiply using Distributive Property. 

7)  (x + 3)(x - 6)

8)  (x + 2)²

9)  (3a² - b)(a² - 2b)

Multiply : 

10)  (x + 3)(x² - 5x + 7)

11)  (a + b)(2a² - 5ab + 3b²)

12)  (2x + 3y)(x² - xy + y²)

Detailed Answer Key

Answer (1) :

=  (4x²)(5x³)

Group factors with like bases together. 

=  (4 ⋅ 5)(x² ⋅ x³)

Use the Product of Powers Property. 

=  20x^{2 + 3}

=  20x⁵

Answer (2) :

=  (a²b²c³)(abc²)

Group factors with like bases together. 

=  (a² ⋅ a)(b² ⋅ b)(c³ ⋅ c²)

Use the Product of Powers Property. 

=  (a^{2 + 1})(b^{2 + 1})(c^{3 + 2})

=  (a³)(b³)(c⁵)

=  a³b³c⁵

Answer (3) :

=  (0.5a³b)(a²c²)(6b²)

Group factors with like bases together. 

=  (0.5 ⋅ 1 ⋅ 6)(a³ ⋅ a²)(b ⋅ b²)c²

Use the Product of Powers Property. 

=  3a^{3 + 2}b^{1 + 2}c²

=  3a⁵b³c²

Answer (4) : 

=  2(3x² + 5x + 7)

Distribute 2.

=  2(3x²) + 2(5x) + 2(7)

Multiply. 

=  6x² + 10x + 14

Answer (5) : 

=  3ab(5a² + b)

Distribute 3ab.

=  3ab(5a²) + 3ab(b)

Group like terms together. 

=  (3 ⋅ 5)(a ⋅ a²)b + 3a(b ⋅ b)

Use the Product of Powers Property. 

=  15a^{1 + 2}b + 3ab^{1 + 1}

=  15a³b + 3ab²

Answer (6) : 

=  2xy(x²y + xz - xy)

Distribute 2xy.

=  2xy(x²y) + 2xy(xz) + 2xy(-xy)

Group like terms together. 

=  2(x ⋅ x²)(y ⋅ y) + 2(x ⋅ x)yz + 2(-1)(x ⋅ x)(y ⋅ y)

Use the Product of Powers Property. 

=  2x^{1 + 2}y^{1 + 1} + 2x^{1 + 1}yz - 2x^{1 + 1}y^{1 + 1}

=  2x³y² + 2x²yz - 2x²y²

Answer (7) : 

=  (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

Answer (8) : 

=  (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

Answer (9) : 

=  (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

Answer (10) :

=  (x + 3)(x² - 5x + 7)

Distributive. 

=  x(x² - 5x + 7) + 3(x² - 5x + 7)

Distribute again. 

=  x(x²) + x(-5x) + x(7) + 3(x²) + 3(-5x) + 3(7)

Simplify. 

=  x³ - 5x² + 7x + 3x² - 15x + 21

Combine the like terms.

=  x³ - 5x²  + 3x²+ 7x - 15x + 21

=  x³ - 2x² - 8x + 21

Answer (11) :

=  (a + b)(2a² - 5ab + 3b²)

Distributive. 

=  a(2a² - 5ab + 3b²) + b(2a² - 5ab + 3b²)

Distribute again. 

=  a(2a²) + a(-5ab) + a(3b²) + b(2a²) + b(-5ab) + b(3b²)

Simplify. 

=  2a³ - 5a²b + 3ab² + 2a² b - 5ab² + 3b³

Combine the like terms.

 =  2a³ - 5a²b + 2a² b - 5ab² + 3ab²+ 3b³

 =  2a³ - 3a²b - 2ab² + 3b³

Answer (12) :

=  (2x + 3y)(x² - xy + y²)

Distribute. 

=  2x(x² - xy + y²) + 3y(x² - xy + y²)

Distribute again.

=  2x(x²) +2x(-xy) + 2x(y²) + 3y(x²) + 3y(-xy) + 3y(y²)

Simplify. 

=  2x³ - 2x²y + 2xy² + 3x²y - 3xy² + 3y³

Combine the like terms.

 =  2x³ + x²y - xy² + 3y³

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