Multiplication of Polynomials Worksheet

**Page 1**

1.

The length and width of a rectangular board are in the ratio 3 : 2. The frame adds 7 inches to the width and 8 inches to the length to form a laminated board. Write a polynomial expression that represents the total area of the board, including the frame.

a. | 6$y$ ^{2} - 21$y$ - 56 | ||

b. | 6$y$ ^{2} + 37$y$ + 56 | ||

c. | 4$y$ ^{2} + 37$y$ - 6 | ||

d. | $y$ ^{2} + $y$ + 3 |

[Lenght : width = 3 : 2.]

After lamination, the length of the rectangular board is 3

[Length is increased by 8 and width by 7.]

Let A be the area of the laminated rectangular board.

A = (length) × (width)

[Area of a rectangle.]

A = (3

[Replace the variables with the values, given.]

A = 3

[Distribute (2

A = 6

[Group the like terms.]

A = 6

[Combine like terms.]

Correct answer : (2)

2.

Evaluate: ($a$ + $z$) ($a$ - $z$) ($a$^{2} + $z$^{2})

a. | - $a$ ^{4} - $z$^{4} | ||

b. | $a$ ^{2} - $z$^{2} | ||

c. | $a$ ^{4} + $z$^{4} | ||

d. | $a$ ^{4} - $z$^{4} |

= (

[Using special product: (

=

[Using special product: (

=

[Simplify.]

Correct answer : (4)

3.

Find:

(2$x$^{$a$} + 6$y$^{$b$}) (3$x$^{$a$} + 5$y$^{$b$})

a. | 6${x}^{2a}+28{x}^{a}{y}^{b}+30{y}^{2b}$ | ||

b. | 6${x}^{2a}+28{x}^{a}{y}^{b}+31{y}^{2b}$ | ||

c. | 5${x}^{2a}+26{x}^{a}{y}^{b}-30{y}^{2b}$ | ||

d. | 6${x}^{2a}-28{x}^{a}{y}^{b}-30{y}^{2b}$ |

= 2

[Distributive property.]

= 6

[

= 6

[Simplify.]

Correct answer : (1)

4.

Find the area of the figure.

a. | (2$y$ ^{2} + 4$y$ +1) sq units | ||

b. | (4$y$ ^{2} + 4$y$ +1) sq units | ||

c. | (2$y$ ^{2} + 2$y$ +1) sq units | ||

d. | (4$y$ ^{2} - 4$y$ +1) sq units |

So, the figure is a square with side 2

Area of a square = side

[Write the formula.]

= (2

Area of the square shown in the figure = (2

[Substitute the value of the side and express the square as product of terms.]

= 2

[Use distributive property.]

= 4

[Multiply the coefficients and add the exponents.]

Area of the figure is (4

Correct answer : (2)

5.

The height of the triangle is 8 times the base $b$ in a right triangle. Find the area of the triangle.

a. | 4$b$ ^{2} square units | ||

b. | 4$b$ square units | ||

c. | 12$b$ ^{2} square units | ||

d. | 8$b$ ^{2} square units |

Area of a triangle =

[Write the formula.]

=

[Substitute the values.]

= 4

[Simplify.]

Area of the right triangle is 4

Correct answer : (1)

6.

What is the degree of the polynomial obtained by calculating the area of a square having a side (3$y$ + 3)?

a. | 1 | ||

b. | 4 | ||

c. | 2 | ||

d. | 3 |

[Write the formula.]

= (3

[Substitute the value.]

= 3

[Use distributive property.]

= 9

[Multiply.]

= 9

[Combine like terms.]

Highest exponent of

The degree of the polynomial obtained by calculating the area of the square is 2.

Correct answer : (3)

7.

Find the area of the unshaded region in the figure.

a. | 23 square units | ||

b. | 32 square units | ||

c. | 45 square units | ||

d. | 56 square units |

Side of the shaded portion is 2 units.

Area of the square with side 6 = (6 x 6) square units

Area of the shaded portion = (2 x 2) square units

Area of the unshaded portion = Area of larger square - Area of the shaded portion

= (6 x 6) - (2 x 2)

[Substitute the values.]

= 36 - 4 = 32

[Multiply and subtract.]

Area of the unshaded portion = 32 square units

Correct answer : (2)

8.

Find the area of the rectangle.

a. | (4$y$ ^{2} - $y$) square units | ||

b. | (4$y$ ^{2} - 4$y$) square units | ||

c. | ($y$ ^{2} - 4) square units | ||

d. | ($y$ ^{2} - 4$y$) square units |

Area of the rectangle = Length x Width

[Write the formula.]

= 2

[Substitute the values.]

= 2

[Use distributive property.]

= 4

[Multiply.]

Area of the rectangle is (4

Correct answer : (2)

9.

Find the area of the rectangle, if the width of the rectangle is 4 more than $\frac{1}{4}$ its length.

a. | ($L$ ^{2} + 4$L$) square units | ||

b. | ($L$ ^{2}/4 + $L$) square units | ||

c. | ($L$ ^{2}/4 - 4$L$) square units | ||

d. | ($L$ ^{2}/4 + 4$L$) square units |

Area of the rectangle = Length x Width

[Write the formula.]

=

[Substitute the values.]

=

[Use distributive property.]

=

[Multiply.]

Area of the rectangle is (

Correct answer : (4)

10.

Write (5$y$^{2} + 20$y$) as a product of two factors.

a. | 5$y$($y$ - 4) | ||

b. | 5$y$ ^{2}($y$ + 4) | ||

c. | 5$y$($y$ + 4) | ||

d. | 5($y$ ^{2} - 5) |

[Original polynomial.]

5

[Express as factors.]

20

[Express as factors.]

5

[Arrange the terms.]

5

[Use distributive property.]

Correct answer : (3)