To get the best deal on Tutoring, call 1-855-666-7440 (Toll Free)

Multiplying Binomials Worksheet

Multiplying Binomials Worksheet
  • Page 1
 1.  
Find the product of the two binomials (3y + 4) and (5y + 4).
a.
15y2 + 32y + 4
b.
15y2 + 20y + 16
c.
3y2 + 32y + 16
d.
15y2 + 32y + 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.]


Correct answer : (4)
 2.  
Evaluate: (3y + 2)(2 - 3y)
a.
(-9y2 + 4)
b.
(9y2 - 4)
c.
(9y2 + 4)
d.
(-9y2 - 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.]


Correct answer : (1)
 3.  
The height of a rectangle is (y - 7) and its base is 3 more than the height. Find the area of rectangle.
a.
y2 + 11y - 28
b.
y2 - 11y + 28
c.
y2 - 11y - 28
d.
y2 + 11y + 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.]


Correct answer : (2)
 4.  
Evaluate: (5y - 3)2
a.
(25y2 - 30y + 9)
b.
(25y2 - 30y - 9)
c.
(25y2 - 15y + 9)
d.
(25y2 - 15y - 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.]


Correct answer : (1)
 5.  
What is the area of the rectangle?


a.
4y2 - 2y + 2
b.
4y2 - 4y - 2
c.
4y2 + 4y - 2
d.
4y2 - 2y - 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.


Correct answer : (4)
 6.  
Multiply the binomials (y + 1 - 5y) and (y + 1).
a.
(-1 - 4y2 + 3y)
b.
(1 - 4y2 - 3y)
c.
(1 + 4y2 + 3y)
d.
(1 + 4y2 - 3y)


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.]


Correct answer : (2)
 7.  
Find the area of the square.

a.
9y2 + 14y + 4
b.
9y2 + 12y + 4
c.
9y2 + 10y + 2
d.
9y2 + 10y + 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.


Correct answer : (2)
 8.  
Expand the expression (y + 3)2.
a.
y2 + 12y + 18
b.
y2 + 12y + 9
c.
y2 + 6y + 9
d.
y2 + 6y + 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.]


Correct answer : (3)
 9.  
The base of a triangle is (10y + 12) m and height is (10y - 7) m. Find the area of the triangle.
a.
(50y2 - 25y + 42) m2
b.
(50y2 + 25y - 42) m2
c.
(50y2 - 25y - 42) m2
d.
(50y2 + 25y + 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.


Correct answer : (2)
 10.  
What is the area of a triangle with a height of 2y - 5 and base equal to 2 times the height of the triangle?
a.
4y2 - 20y + 25
b.
4y2 + 20y + 25
c.
4y2 - 20y + 50
d.
4y2 + 20y + 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.


Correct answer : (1)

*AP and SAT are registered trademarks of the College Board.