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:  5n²,  x⁸,  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

 

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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