Multiplying and Dividing Polynomials Symbolically

Multiplying or dividing two monomials will produce another monomial. To multiply two monomials, multiply the coefficients and then multiply the variables.

Example 8

Recall that exponents are added when multiplying powers.

Simplify the expression .

 



Example 9

Simplify the expression .



Dividing monomials is similar to multiplying monomials. To divide two monomials, divide the coefficients and then divide the variables.

Example 10
Recall that exponents are subtracted when dividing powers.

Simplify the expression .

 


 

Example 11

Simplify the expression .


To multiply a monomial by a binomial, the distributive property is used.

Distributive Property
a rule that states a( b + c) = ab + ac.
For example, 4(10 + 6) = (4)(10) + (4)(6).

Example 12

Simplify the expression .