1. Objective
Multiply two binomials.

2. Group factors with like bases together. (4x3)(6x7)
Check It Out! Example 1
Multiply.
a. (4x3)(6x7)
Group factors with like bases together.
(4x3)(6x7)
(4 6)(x3 x7) 
Multiply.
24x10
b. (3rt4)(5t3)
Group factors with like bases together.
(3rt4)(5t3)
(3 5)(r)(t4 t3) 
Multiply.
15rt7

3. Check It Out! Example 2
Multiply.
b. 2ab(5a5 + b)
3ab(5a2 + b)
Distribute 3ab.
(3ab)(5a2) + (3ab)(b)
Group like bases together.
(3  5)(a  a2)(b) + (3)(a)(b  b)
15a3b + 3ab2
Multiply.

4. To multiply a binomial by a binomial, you can apply the Distributive Property more than once:
(x + 3)(x + 2) = x(x + 2) + 3(x + 2)
Distribute x and 3.
Distribute x and 3 again.
= x(x + 2) + 3(x + 2)
= x(x) + x(2) + 3(x) + 3(2)
Multiply.
= x2 + 2x + 3x + 6
Combine like terms.
= x2 + 5x + 6

5. Example 3A: Multiplying Binomials
(s + 4)(s – 2)
(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 – 8
Multiply.
s2 + 2s – 8
Combine like terms.

6. Example 3C: Multiplying Binomials
(8m2 – n)(m2 – 3n)
Use the FOIL method.
8m2(m2) + 8m2(–3n) – n(m2) – n(–3n)
8m4 – 24m2n – m2n + 3n2
Multiply.
8m4 – 25m2n + 3n2
Combine like terms.

7. Check It Out! Example 3c
Multiply.
(2a – b2)(a3 + 4b2)
(2a – b2)(a3 + 4b2)
Use the FOIL method.
2a(a3) + 2a(4b2) – b2(a3) + (–b2)(4b2)
2a4 + 8ab2 – a3b2 – 4b4
Multiply.