﻿ Multiplication Worksheets - Page 2 | Problems & Solutions

# Multiplication Worksheets - Page 2

Multiplication Worksheets
• Page 2
11.
Find the product of 2$y$3 + 5$y$ - 2$y$2 and 2$y$.
 a. 4$y$4 - $y$3 - $y$2 b. 4$y$4 + 10$y$3 - $y$2 c. 4$y$4 - 4$y$3 + 10$y$2 d. None of the above

#### Solution:

2y3 + 5y - 2y2, 2y.
[Original expressions.]

2y x (2y3 + 5y - 2y2).
[Multiply the expressions.]

= 2y(2y3) + 2y(5y) - 2y(2y2)
[Use distributive property.]

= 2(2)y4 + 2(5)y2 - 2(2)y3
[Evaluate exponents.]

= 4y4 + 10y2 - 4y3
[Multiply.]

The product of 2y3 + 5y - 2y2 and 2y is 4y4 - 4y3 + 10y2.

12.
Find the area of the rectangle.

 a. $x$2 + $x$ + 8 b. $x$2 + 6$x$ + 8 c. 2$x$2 + 6$x$ + 6 d. $x$2 - $x$ + 8

#### Solution:

From the figure, the length and the width of the rectangle are (x + 4) and (x + 2), respectively.

Area of the rectangle = length x width = (x + 4)(x + 2)

The product has one x2 tile, six x tiles and eight 1-tiles.

So, the area of the rectangle is (x2 + 6x + 8).

13.
Find the product of $k$ + $k$3 + 2 and $k$3 + 2.
 a. k6 + k4 + 3k3 + 2k + 4 b. k6 + k3 + 4k4 + 2k + 4 c. k6 + k4 + 4k3 + k + 4 d. k6 + k4 + 4k3 + 2k + 4

#### Solution:

(k + k3 + 2)(k3 + 2)
[Original polynomials.]

= k(k3 + 2) + k3(k3 + 2) + 2(k3 + 2)
[Use distributive property.]

= k(k3) + k(2) + k3(k3) + k3(2) + 2(k3) + 2(2)
[Use distributive property.]

= k4 + 2k + k6 + 2k3 + 2k3 + 4
[Multiply monomials.]

= k6 + k4 + 4k3 + 2k + 4
[Combine like terms and write the resultant expression in standard form.]

So, the product of k + k3 + 2 and k3 + 2 is k6 + k4 + 4k3 + 2k + 4.

14.
Find the product of 3$b$2 - 5$b$ - 1 and $b$ - 1.
 a. 3b3 - 8b2 - 4b + 1 b. 3b3 + 8b2 + 4b + 1 c. 3b3 - 8b2 + 4b + 1 d. 3b3 + 8b2 - 4b + 1

#### Solution:

(3b2 - 5b - 1)(b - 1)
[Original polynomials.]

= 3b2(b - 1) - 5b(b - 1) - 1(b - 1)
[Use distributive property.]

= 3b2(b) + 3b2(-1) - 5b(b) - 5b(-1) - 1(b) - 1(-1)
[Use distributive property.]

= 3b3 - 3b2 - 5b2 + 5b - b + 1
[Multiply monomials.]

= 3b3 - 8b2 + 4b + 1
[Combine like terms.]

So, the product of 3b2 - 5b - 1 and b - 1 is 3b3 - 8b2 + 4b + 1.

15.
Find the product of ($b$3 + $b$2 + 5$b$ + 6) and (1 - $b$).
 a. -b4 + 4b2 - b + 6 b. -b4 - 4b2 + b + 6 c. -b4 - 4b2 - b + 6 d. b4 - 4b2 - b + 6

#### Solution:

(b3 + b2 + 5b + 6)(1 - b)
[Original polynomials.]

= b3(1 - b) + b2(1 - b) + 5b(1 - b) + 6(1 - b)
[Use distributive property.]

= b3(1) + b3(-b) + b2(1) + b2(-b) + 5b(1) + 5b(-b) + 6(1) + 6(-b)
[Use distributive property.]

= b3 - b4 + b2 - b3 + 5b - 5b2 + 6 - 6b
[Multiply monomials.]

= (b3 - b3) - b4 + (b2 - 5b2) + (5b - 6b) + 6
[Group like terms.]

= -b4 - 4b2 - b + 6
[Combine like terms.]

(b3 + b2 + 5b + 6)(1 - b) = -b4 - 4b2 - b + 6.

16.
Find the product: (3$a$ + 4$a$2)$a$
 a. 3a3 - 4a2 b. 3a2 - 4a3 c. 3a2 + 4a3 d. 3a3 + 4a2

#### Solution:

(3a + 4a2)a
[Original polynomials.]

= 3a(a) + 4a2(a)
[Use distributive property.]

= 3a2 + 4a3
[Multiply monomials.]

(3a + 4a2)a = 3a2 + 4a3 .

17.
Find the area of a rectangle, if its length is 3$x$ + 1 and its width is $x$ + 3 units.
 a. 3x2 + 10x - 3 b. 3x2 - 10x - 3 c. 3x2 + 10x + 3 d. 3x2 - 10x + 3

#### Solution:

Area of the rectangle = length x width

= (3x + 1)(x + 3)
[Substitute the length and width.]

= 3x(x + 3) + 1(x + 3)
[Use distributive property.]

= 3x2 + 9x + x + 3
[Multiply.]

= 3x2 + 10x + 3
[Combine like terms.]

So, the area of the rectangle is 3x2 + 10x + 3 square units.

18.
Find the product of - 4$y$ and ($y$2 + 3$y$ - 2).
 a. 4$y$3 + 8$y$2 - 12 b. -4$y$3 - 12$y$2 + 8$y$ c. 4$y$3 - 12$y$2 + 8$y$ d. None of the above

#### Solution:

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

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

= -4y x y2 - 4y x 3y + 4y x 2
[Use distributive property.]

= -4y3 - 12y2 + 8y
[Simplify.]

The product of -4y and (y2 + 3y - 2) is -4y3 - 12y2 + 8y.

19.
Find the product of 4$y$3 + 4$y$ + 3$y$2 and 3$y$.
 a. 12$y$4 + 9$y$3 + 12$y$2 b. 12$y$4 - 12$y$3 - $y$2 c. 12$y$4 - $y$3 - $y$2 d. None of the above

#### Solution:

4y3 + 4y + 3y2, 3y.
[Original expressions.]

3y x (4y3 + 4y + 3y2).
[Multiply the expressions.]

= 3y(4y3) + 3y(4y) + 3y(3y2)
[Use distributive property.]

= 3(4)y4 + 3(4)y2 + 3(3)y3
[Evaluate exponents.]

= 12y4 + 12y2 + 9y3
[Multiply.]

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

20.
Find the area of the figure.

 a. (4$y$2 - 4$y$ +1) sq units b. (4$y$2 + 4$y$ +1) sq units c. (2$y$2 + 4$y$ +1) sq units d. (2$y$2 + 2$y$ +1) sq units

#### Solution:

The two adjacent sides of the figure are equal.

So, the figure is a square with side 2y + 1.

Area of a square = side2
[Write the formula.]

= (2y + 1)(2y + 1)
Area of the square shown in the figure = (2y + 1)2
[Substitute the value of the side and express the square as product of terms.]

= 2y(2y + 1) + 1(2y + 1)
[Use distributive property.]

= 4y2 + 4y + 1
[Multiply the coefficients and add the exponents.]

Area of the figure is (4y2 + 4y +1) sq units.