Multiplying and Dividing Polynomials

Multiplying Monomials

100

(3y)(7y)

21y²

200

(3a)(-8ab)

-24a²b

300

(-5q²r)(-4q)

20q³r

400

(-10m⁴n⁷)(-3m⁴n) 

30m⁸n⁸

500

(2ab²c²)(4a³b²c²)

8a⁴b⁴c⁴

Multiplying Polynomials

100

2x²(3x² + 7)

6x⁴ + 14x²

200

4e³(2e⁵ + 5)

8e⁸ + 20e³

300

(-3w)(w + 3y - 2) 

-3w² - 9wy + 6w

400

a²b⁴c⁵(7a⁵b⁹c¹⁰d¹³ - 9abce²f)

7a⁷b¹³c¹⁵d¹³ - 9a³b⁵c⁶e²f

500

7ab²c⁷(7b⁴c⁹g⁴v⁷ - 9a)

49ab⁶c¹⁶g⁴v⁷ - 63a²b²c⁷

Dividing Monomials

100

(16x²) ÷ (4x²)

4

200

-40m
-8m

5

300

(8x⁵y²) ÷ (-8x²y)

-x³y

400

-63s³tu⁹
7s²tu⁵

-9su⁴

500

-96p⁷q⁵r
-4p⁵q⁴

24p²qr

Dividing Polynomials

100

(15x² - 10x³) ÷ (x)

15x - 10x²

200

16y² + 8y
8y

2y + 1

300

(6n² + 12n⁷ - 9n) ÷ (3n)

2n + 4n⁶ - 3

400

42x²y + 24x⁴y⁶ 
0.5xy

84x+ 48x³y⁵

500

(0.3xy⁴z¹⁰ - 18x⁷y³z⁶) ÷ (0.1xyz³)

3y³z⁷ - 180x⁶y²z³

Word Problems

100

The area of a rectangle is 72d² and its length is 6d. What is an expression for its width?

12d

200

The base of a triangle is 10p and the height is 4p. What is the area of the triangle? 

20p²

300

A rectangular packing crate has the following dimensions: length=2x width=x height=2x+2

What is an expression for the volume? 

4x³+4x²

400

A rectangle has an area of 9x² - 3x square units. The width of the rectangle is 3x units. What is the length?

3x-1

500

A rectangular wall has a circular window. The area of the wall can be represented by 32x² + 16x. The length of the wall is 8x. The diameter of the circular window has a measurement that is half the width of the wall. What is the radius of the window written as an expression in terms of x?

x+1/2 or x+0.5