To multiply one monomial by another, we multiply the numerical factors and then multiply the variable factors.
Example 1: Perform each multiplication:
Multiplying a Polynomial by a Monomial
To multiply a polynomial by a monomial, we use the distributive property and multiply each term of the polynomial by the monomial.
Example 2: Perform each multiplication:
Multiplying a Polynomial by a Polynomial
To multiply a polynomial by a polynomial, we use the distributive property repeatedly.
Example 3: Perform each multiplication:
Example 6: Find each square:
Example 7: Multiply:
The products discussed in Examples 6 and 7 are called
special products. The two trinomials are called
perfect square trinomials.
Example 9: Multiply:
An Application of Multiplying Polynomials
Recall: Area formulas:
Example: Write a polynomial that represents the area of the rectangle shown:
Multiplying Expressions that are not Polynomials
Example 11: Find the product of