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 x 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.



Example 2:

Multiply: (8x3y7)(3x5y4)

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

8 x 3 = 24

Step 2:   Multiply like variables. 

x3 x5 ) =  x8

y7 ( y4 ) =  y11

Final Answer:   Combine the constants and variables.