1. Multiply polynomials
When multiplying powers with the same base, keep the base and add the exponents.
x2  x3 = x2+3 = x5
Example 1: Multiplying Monomials
A. (6y3)(3y5)
(6y3)(3y5) Group factors with like bases together.
(6 ● 3)(y3 ● y5) Group factors with like bases together. Multiply
18y Multiply
B. (3mn2) (9m2n)
(3mn2)(9m2n) Group factors with like bases together.
(3 ● 9)(m ● m2)(n2 ● n) Group factors with like bases together.
27m3n Multiply

2. To multiply a polynomial by a monomial, use the Distributive Property.
Example 2: Multiplying a Polynomial by a Monomial
C. 3ab(5a2 + b)
3ab(5a2 + b)
(3ab)(5a2) + (3ab)(b) Distribute 3ab.
(3  5)(a  a2)(b) + (3)(a)(b  b) Group like bases together.
15a3b + 3ab Multiply
Example 3A: Multiplying a Binomial by a Binomial
To multiply a binomial by a binomial, you can apply the Distributive Property more than once:
D. (x + 3)(x + 2) = x(x + 2) + 3(x + 2) Distribute x and 3.
= x(x + 2) + 3(x + 2) Distribute x and 3 again.
= x(x) + x(2) + 3(x) + 3(2) Multiply
= x2 + 2x + 3x Combine like terms.
= x2 + 5x + 6

3. 1. Multiply the First terms. (x + 3)(x + 2) x x = x2
Example 3B: Multiplying a Binomial by a Binomial
Another method for multiplying binomials is called the FOIL method.
1. Multiply the First terms. (x + 3)(x + 2) x x = x2 
2. Multiply the Outer terms. (x + 3)(x + 2) x 2 = 2x 
3. Multiply the Inner terms. (x + 3)(x + 2) x = 3x 
4. Multiply the Last terms. (x + 3)(x + 2) = 6 
(x + 3)(x + 2) = x2 + 2x + 3x + 6 = x2 + 5x + 6 F O I L

4. (s + 4)(s – 2)
s(s – 2) + 4(s – 2) Distribute s and 4.
s(s) + s(–2) + 4(s) + 4(–2) Distribute s and 4 again.
s2 – 2s + 4s – Multiply
s2 + 2s – Combine like terms.