﻿ Multiplication Worksheets | Problems & Solutions

# Multiplication Worksheets

Multiplication Worksheets
• Page 1
1.
What is the product of 7$y$ and 7$y$?
 a. 45$y$2 b. 55$y$2 c. 53$y$2 d. 49$y$2

#### Solution:

7y x 7y
[Original monomials.]

= 7 x 7 x y x y
[Rearrange factors.]

= 49 x y x y
[Multiply coefficients.]

= 49y2

2.
Evaluate the expression (7$y$2 - 2$y$ - 5)(5$y$2 - 5$y$ - 4), for $y$ = 2.
 a. 112 b. 114 c. 116 d. 118

#### Solution:

(7y2 - 2y - 5)(5y2 - 5y - 4)
[Original expression.]

= [7(2)2 - 2(2) - 5][5(2)2 - 5(2) - 4]
[Replace the variable with the value, given.]

= [7(4) - 2(2) - 5][5(4) - 5(2) - 4]
[Evaluate the exponents.]

= (28 - 4 - 5)(20 - 10 - 4)
[Simplify.]

= (19)(6)

= 114
[Multiply.]

3.
Find the product of 3$y$4 and 4$y$5.
 a. 9$y$9 b. 15$y$9 c. 12$y$8 d. 12$y$9

#### Solution:

3y4 , 4y5
[Original polynomials.]

(3y4) x (4y5)
[Multiply the two polynomials.]

= 3 x 4 x y4 x y5
[Rearrange the factors.]

= 12y9

The product of 3y4 and 4y5 is 12y9.

4.
Find the product of 3$y$ and (3$y$2 - 1).
 a. 9$y$3 - 3$y$ b. -9$y$3 - 3$y$ c. -9$y$3 + $y$ d. 9$y$3 + 3$y$

#### Solution:

3y, (3y2 - 1)
[Original polynomials.]

(3y) x (3y2 - 1)
[Multiply the two polynomials.]

= 3y(3y2) + 3y(-1)
[Use distributive property.]

= 9y3 - 3y
[Multiply monomials.]

The product of 3y and (3y2 - 1) is 9y3 - 3y.

5.
Find the product of (- $y$ + 4) and (- $y$ - 4).
 a. -$y$2 - $y$ + 16 b. -$y$2 + 16 c. $y$2 + 16$y$ - 1 d. $y$2 - 16

#### Solution:

(-y + 4) and (-y - 4)
[Original polynomials.]

(-y + 4) x (-y - 4)
[Multiply the two polynomials.]

= -y (-y - 4) + 4(-y - 4)
[Use distributive property.]

= -y (-y) + 4y - 4y + 4(-4)
[Use distributive property.]

= y2 - 4y + 4y - 16
[Multiply.]

= y2 - 16
[Combine like terms.]

The product of (-y + 4) and (-y - 4) is y2 - 16.

6.
Find the product of - 4$y$ and ($y$2 - 2$y$ - 2).
 a. 4$y$3 - 8$y$2 - 8$y$ b. 4$y$3 + 8$y$2 + 8 c. -4$y$3 + 8$y$2 + 8$y$ d. None of the above

#### Solution:

-4y, (y2 - 2y - 2)
[Original polynomials.]

-4y x (y2 - 2y - 2)
[Multiply the two polynomials.]

= -4y x y2 + 4y x 2y + 4y x 2
[Use distributive property.]

= -4y3 + 8y2 + 8y
[Simplify.]

The product of -4y and (y2 - 2y - 2) is -4y3 + 8y2 + 8y.

7.
Find the product of ($y$ + 2) and ($y$ - 2).
 a. -$y$2 - 4 b. -$y$2 + 4 c. $y$2 + 4 d. $y$2 - 4

#### Solution:

(y + 2), (y - 2)
[Original polynomials.]

(y + 2) x (y - 2)
[Multiply the two polynomials.]

= (y x y) - 2y + 2y - 4
[Use distributive property.]

= y2 - 4

The product of (y + 2) and (y - 2) is y2 - 4.

8.
Find the product of (4$y$2 + 3$y$) and (3$y$2 - 3$y$).
 a. 12$y$4 - 3$y$3 - 9$y$2 b. 4$y$4 - 3$y$3 - $y$2 c. $y$4 + 4$y$3 - 12$y$2 d. None of the above

#### Solution:

(4y2 + 3y) , (3y2 - 3y)
[Original polynomials.]

(4y2 + 3y) x (3y2 - 3y).
[Multiply the two polynomials.]

= (4y2 x 3y2 - 4y2 x 3y + 3y x 3y2 -3y x 3y)
[Use distributive property.]

= (12 x y2 x y2 - 3 x y2 x y - 9 x y x y)
[Use distributive property.]

= (12y4 - 3y3 - 9y2)

The product of (4y2 + 3y) and (3y2 - 3y) is (12y4 - 3y3 - 9y2).

9.
Find the product of - 3$y$ and ($y$3 - 4$y$2 - $y$ - 2).
 a. -3$y$4 - 6$y$3 - 3$y$2 + 12$y$ b. 1 - 3$y$4 c. -3$y$4 + 12$y$3 + 3$y$2 + 6$y$ d. None of the above

#### Solution:

-3y, (y3 - 4y2 - y - 2)
[Original polynomials.]

-3y x (y3 - 4y2 - y - 2)
[Multiply the two polynomials.]

= -3 x y x y3 + 12 x y x y2 + 3 x y x y + 6 x y
[Use distributive property.]

= -3y4 + 12y3 + 3y2 + 6y

The product of -3y and (y3 - 4y2 - y - 2) is -3y4 + 12y3 + 3y2 + 6y.

10.
Find the product of (2$y$2 + 5) and ($y$2 - 6).
 a. 2$y$4 - 7$y$2 - 30 b. 2$y$4 + 5$y$2 - 5 c. 2$y$4 + 6$y$2 + 30 d. 2$y$4 - $y$2 - 12

#### Solution:

(2y2 + 5), (y2 - 6)
[Original polynomials.]

(2y2 + 5) x (y2 - 6)
[Multiply the two polynomials.]

= 2y2(y2 - 6) + 5(y2 - 6)
[Use distributive property.]

= 2y2(y2) + 2y2(-6) + 5(y2) + 5(-6)
[Use distributive property.]

= 2y4 - 12y2 + 5y2 - 30
[Multiply.]

= 2y4 - 7y2 - 30
[Combine like terms.]

The product of (2y2 + 5) and (y2 - 6) is 2y4 - 7y2 - 30.