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Multiplying Polynomials

Multiplying Monomials

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:

Special Products

Example 6: Find each square:

Graphical Illustration:

Example 7: Multiply:

The products discussed in Examples 6 and 7 are called special products. The two trinomials are called
perfect square trinomials.

*Note:

Example 9: Multiply:

An Application of Multiplying Polynomials

Recall: Area formulas:

Square

Rectangle

Triangle

Example: Write a polynomial that represents the area of the rectangle shown:

Multiplying Expressions that are not Polynomials

Example 11: Find the product of and