Multiplying PolynomialsMultiplying Polynomials

Section 10.3

Multiplying MonomialsMultiplying Monomials

To multiply two monomials use the To multiply two monomials use the associative and commutative associative and commutative properties and regroup. Remember properties and regroup. Remember that to multiply exponential that to multiply exponential expressions with a common base, add expressions with a common base, add exponents.exponents.

( )( ) 4 63 5x x Use the commutative and associative properties. 4 6 3 5a fa f( )( )x x

24 3 5x Use the product rule for exponents.

24 8x Simplify.

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Multiplying Monomials by Multiplying Monomials by PolynomialsPolynomials

To multiply a monomial and any To multiply a monomial and any polynomial, we use the distributive polynomial, we use the distributive property property and properties of and properties of exponents. exponents.

a(b c) a • b a • c

3Martin-Gay, Prealgebra, 5ed

Multiplying Monomials by Multiplying Monomials by Polynomials. . .Polynomials. . .

3x(5x2 4) 3x • 5x2 3x • 4 15x3 12x

Apply the distributive property.Apply the distributive property.

4z(2z

2 5z – 6) 4z • 2z

2 4z • 5z 4z • (- 6) 8z

3 20z

2 – 24z

4Martin-Gay, Prealgebra, 5ed

To multiply two binomials, we use a version of To multiply two binomials, we use a version of the distributive property.the distributive property.

(b c)a b • a c • a

Multiplying Two PolynomialsMultiplying 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 65

To Multiply Two PolynomialsTo Multiply Two Polynomials

Multiply each term of the first polynomial by each term of the second polynomial and then combine like terms.

6Martin-Gay, Prealgebra, 5ed