# Multiplying Binomials Worksheet

Multiplying Binomials Worksheet
• Page 1
1.
Find the product of the two binomials (3$y$ + 4) and (5$y$ + 4).
 a. 15$y$2 + 32$y$ + 4 b. 15$y$2 + 20$y$ + 16 c. 3$y$2 + 32$y$ + 16 d. 15$y$2 + 32$y$ + 16

#### Solution:

(3y + 4)(5y + 4)
[Original expression.]

= 3y(5y + 4) + 4(5y + 4)
[Use distributive property.]

= 15y2 + 12y + 20y + 16
[Multiply.]

= 15y2 + 32y + 16
[Combine like terms.]

2.
Evaluate: (3$y$ + 2)(2 - 3$y$)
 a. (-9$y$2 + 4) b. (9$y$2 - 4) c. (9$y$2 + 4) d. (-9$y$2 - 4)

#### Solution:

(3y + 2)(2 - 3y)
[Given expression.]

= 3y(2 - 3y) + 2(2 - 3y)
[Use distributive property.]

= 6y - 3y(3y) + 4 - 2(3y)
[Use distributive property.]

= 6y - 9y2 + 4 - 6y
[Simplify.]

= -9y2 + 4
[Combine like terms and arrange in the standard form.]

3.
The height of a rectangle is ($y$ - 7) and its base is 3 more than the height. Find the area of rectangle.
 a. $y$2 + 11$y$ - 28 b. $y$2 - 11$y$ + 28 c. $y$2 - 11$y$ - 28 d. $y$2 + 11$y$ + 28

#### Solution:

Area of rectangle = base x height.

Height of rectangle is (y - 7) and base of a rectangle is 3 more than the height = y - 7 + 3 = y - 4

Area = (y - 7)(y - 4)
[Substitute the values.]

= y(y - 4) - 7(y - 4)
[Distributive property.]

= y(y) - 4y - 7y + 7(4)
[Distributive property.]

= y2 - 4y - 7y + 28
[Multiply.]

= y2 - 11y + 28
[Combine like terms.]

4.
Evaluate: (5$y$ - 3)2
 a. (25$y$2 - 30$y$ + 9) b. (25$y$2 - 30$y$ - 9) c. (25$y$2 - 15$y$ + 9) d. (25$y$2 - 15$y$ - 9)

#### Solution:

(5y - 3)2
[Original polynomial.]

= (5y - 3)(5y - 3)
[Split into two terms.]

= 5y(5y - 3) - 3(5y - 3)
[Use distributive property.]

= 25y2 - 15y - 15y + 9
[Multiply.]

= 25y2 - 30y + 9
[Combine like terms.]

5.
What is the area of the rectangle?

 a. 4$y$2 - 2$y$ + 2 b. 4$y$2 - 4$y$ - 2 c. 4$y$2 + 4$y$ - 2 d. 4$y$2 - 2$y$ - 2

#### Solution:

The sides of the rectangle are 2y - 2 and 2y + 1.

The area of a rectangle = the product of its sides.

The area of the rectangle = (2y - 2)(2y + 1)
[Substitute the values.]

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

= 4y2 + 2y - 4y - 2
[Multiply.]

= 4y2 - 2y - 2
[Combine like terms.]

The area of the rectangle is 4y2 - 2y - 2.

6.
Multiply the binomials ($y$ + 1 - 5$y$) and ($y$ + 1).
 a. (-1 - 4$y$2 + 3$y$) b. (1 - 4$y$2 - 3$y$) c. (1 + 4$y$2 + 3$y$) d. (1 + 4$y$2 - 3$y$)

#### Solution:

(y + 1 - 5y) (y + 1)
[Original binomials.]

= (1 - 4y)(y + 1)
[Combine like terms.]

= 1(y + 1) - 4y (y + 1)
[Use the distributive property.]

= y + 1 - 4y2 - 4y
[Multiply.]

= 1 - 4y2 - 3y
[Combine like terms.]

7.
Find the area of the square.

 a. 9$y$2 + 14$y$ + 4 b. 9$y$2 + 12$y$ + 4 c. 9$y$2 + 10$y$ + 2 d. 9$y$2 + 10$y$ + 4

#### Solution:

The side of the square is 3y + 2.

The area of a square = side2

The area of the square = (3y + 2)(3y + 2)
[Substitute the values.]

= 3y(3y + 2) + 2(3y + 2)
[Use distributive property.]

= 9y2 + 6y + 6y + 4
[Multiply.]

= 9y2 + 12y + 4
[Combine like terms.]

The area of the square is 9y2 + 12y + 4.

8.
Expand the expression ($y$ + 3)2.
 a. $y$2 + 12$y$ + 18 b. $y$2 + 12$y$ + 9 c. $y$2 + 6$y$ + 9 d. $y$2 + 6$y$ + 18

#### Solution:

(y + 3)2
[Original expression.]

= (y + 3)(y + 3)
[Split into two terms.]

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

= y2 + 3y + 3y + 9
[Multiply.]

= y2 + 6y + 9
[Combine like terms.]

9.
The base of a triangle is (10$y$ + 12) m and height is (10$y$ - 7) m. Find the area of the triangle.
 a. (50$y$2 - 25$y$ + 42) m2 b. (50$y$2 + 25$y$ - 42) m2 c. (50$y$2 - 25$y$ - 42) m2 d. (50$y$2 + 25$y$ + 42) m2

#### Solution:

Let A be the area of the triangle.

Area = 12 x base x height
[Write the formula.]

A = 12 x (10y + 12) x (10y - 7)
[Substitute the values.]

A = 12[10y(10y) - 7(10y) + 12(10y) - 12(7)]
[Use the distributive property.]

A = 12(100y2 - 70y + 120y - 84)
[Multiply.]

A = 12(100y2 + 50y - 84)
[Combine like terms.]

= 50y2 + 25y - 42
[Divide each term of the expression by 2.]

Area of the triangle is (50y2 + 25y - 42) m2.

10.
What is the area of a triangle with a height of 2$y$ - 5 and base equal to 2 times the height of the triangle?
 a. 4$y$2 - 20$y$ + 25 b. 4$y$2 + 20$y$ + 25 c. 4$y$2 - 20$y$ + 50 d. 4$y$2 + 20$y$ + 50

#### Solution:

The base of the triangle = 2 x height = 2 x (2y - 5).
[Since height = (2y - 5).]

The area of a triangle = 1 / 2 x base x height.
[Formula.]

The area of the triangle = 1 / 2 x 2(2y - 5) x (2y - 5)
[Substitute the values.]

= (2y - 5)(2y - 5)
[Divide out the common factor, 2.]

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

= 4y2 - 10y - 10y + 25
[Multiply.]

= 4y2 - 20y + 25
[Combine like terms.]

The area of the triangle is 4y2 - 20y + 25.