Multiplying Polynomials Section 10.3

Multiplying Monomials To multiply two monomials use the associative and commutative properties and regroup. Remember that to multiply exponential expressions with a common base, add exponents. Use the commutative and associative properties. Use the product rule for exponents. Simplify. 2

Multiplying Monomials by Polynomials To multiply a monomial and any polynomial, we use the distributive property and properties of exponents. a(b  c)  a b  a c 3 Martin-Gay, Prealgebra, 5ed

Multiplying Monomials by Polynomials... 3x(5x 2  4)  3x 3x 5x2 5x2  3x 3x 4  15x 3  12x Apply the distributive property. 4z(2z 2  5z 5z – 6)  4z 4z 2z 2z 2  4z 4z 5z 5z  4z 4z (- (- 6)  8z 8z 3  20z 2 – 24z 4 Martin-Gay, Prealgebra, 5ed

To multiply two binomials, we use a version of the distributive property. (b  c)a  b a  c a Multiplying Two Polynomials (x  2)(x  3)  x(x  3)  2(x  3)  x x  x 3  2 x  2 3  x 2  3x  2x  6  x 2  5x  6 5

To Multiply Two Polynomials Multiply each term of the first polynomial by each term of the second polynomial and then combine like terms. 6 Martin-Gay, Prealgebra, 5ed