Multiplying Polynomials

1
Multiplying Polynomials
Section 10.3
2
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.
3
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
Martin-Gay, Prealgebra, 5ed
4
Multiplying Monomials by Polynomials. . .
Apply the distributive property.
3x(5x2 4)
3x 5x2 3x 4 15x3 12x
4z(2z 2 5z 6)
4z 2z 2 4z 5z 4z (- 6) 8z 3 20z 2
24z
Martin-Gay, Prealgebra, 5ed
5
Multiplying Two Polynomials

• To multiply two binomials, we use a version of
  the distributive property.
• (b c)a b a c a

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