2. M ULTIPLYING P OLYNOMIALS Adapted from Walch Education

3. K EY C ONCEPTS To multiply two polynomials, multiply each term in the first polynomial by each term in the second. The Distributive Property can be used to simplify the product of two or more polynomials. FOIL- another way to represent the product ( a + b )( c + d ) = ac + ad + bc + bd. 2 4.2.2: Multiplying Polynomials

4. K EY C ONCEPTS, CONTINUED If either polynomial has three or more terms, i.e ( a + b + c )( d + e + f ) = ( a + b + c ) d + ( a + b + c ) e + ( a + b + c ) f = ad + bd + cd + ae + be + ce + af + bf + cf. To find the product of a variable with a coefficient and a numeric quantity, multiply the coefficient by the numeric quantity. If a and b are real numbers, then ax b = abx. 3 4.2.2: Multiplying Polynomials

5. K EY C ONCEPTS, CONTINUED To find the product of two variables raised to a power, use the properties of exponents. If the bases are the same, add the exponents: x n x m = x n + m. If the bases are not the same, then the exponents cannot be added. x n y m = x n y m. After multiplying all terms, simplify the expression by combining like terms. The product of two polynomials is a polynomial, so the system of polynomials is closed under multiplication. 4 4.2.2: Multiplying Polynomials

6. P RACTICE ( IN CLASS ) 1. Find the product of ( x 3 + 9 x )(– x 2 + 11). 2. Find the product of (3 x + 4)( x 2 + 6 x + 10). 5 4.2.2: Multiplying Polynomials

7. T HANKS FOR W ATCHING !!! ~Ms. Dambreville