Multiply Monomials

Multiply Monomials

A monomial is a single term that can include any combination of the following:  a constant, a variable, exponent(s), or multiplication.

Examples of monomials:  5n2x8,  29ab3

Monomials cannot include addition or subtraction signs.

So the following are NOT monomials:  4x + 3y,   18m − 3r

Multiplying Monomials

There are two steps to follow when multiplying monomials:

• Multiply the coefficients (constants).
• Multiply the variables.

Example 1:

Multiply: (4y 2)(5y 3)

Step 1:  Identify and then multiply the coefficients.

The coefficients are 4 and 5.  4 × 5 = 20.

Step 2:   Multiply the variables.

The variables are y2 and y3.  When multiplying two terms with the same base, you add the exponents.

y2 (y3) = y5

Final Answer:  Combine the constants and variables.

20y5

Example 2:

Multiply: (8x3y7)(3x5y4)

Step 1:   Identify and multiply the coefficients, which are 8 and 3.

8 × 3 = 24

Step 2:   Multiply like variables.

x3 x5 ) =  x8

y7 ( y4 ) =  y11

Final Answer:   Combine the constants and variables.

24x8y11

Practice

1)   Multiply: (9x)(6x3)

2)  Multiply: (3x2y3)(7x4y5)

3)  Multiply: (3x2y2r2)(6xyr4)

4)  Multiply: (5x2)2(3x3)3

5)  Multiply: (9xy4t)2(4x2yt3)4

Answers

1.)  54x4

2.)  21x6y8

3.)  18x3y3r 6

4.)  675x13

5.)  20736x10y12t14