1. 8-3 Multiplying Binomials
Hubarth
Algebra

2. Ex 1 Using the Distributive Property
Simplify (2y – 3)(y + 2).
(2y – 3)(y + 2) = (2y – 3)(y) + (2y – 3)(2) Distribute 2y – 3.
= 2y2 – 3y + 4y – 6 Now distribute y and 2.
= 2y2 + y – 6 Simplify.

3. Another way to multiply binomials is by FOIL.
F- multiply the FIRST terms in each binomial.
O- multiply the OUTER most terms of each binomial
I- multiply the inner most terms of each binomial
L- multiply the last terms in each binomial
Ex 2 Multiplying Using FOIL
Simplify (4x + 2)(3x – 6).
First
= (4x)(3x)
(4x + 2)(3x – 6)
Outer
(4x)(–6) +
Last
(2)(–6) +
Inner
(2)(3x) +
24x 6x 12 – +
= 12x2
= 12x2
18x – 12
The product is 12x2 – 18x – 12.

4. Ex 3 More FOIL
Simplify (x + 2)(3x – 2) F
3x(x) O
x(-2) I
2(3x) L
2(-2) + + +
3𝑥 2 −2𝑥+6𝑥−4
3 𝑥 2 +4𝑥−4

5. Ex 4 Multiplying a Trinomial and a Binomial
Simplify the product (3x2 – 2x + 3)(2x + 7).
= (2x)(3x2) – (2x)(2x) + (2x)(3) + (7)(3x2) – (7)(2x) + (7)(3)
(2x + 7)(3x2 – 2x + 3)
= 6x3 – 4x2 + 6x + 21x2 – 14x + 21
= 6x3 + 17x2 – 8x + 21
The product is 6x3 + 17x2 – 8x + 21.

6. Practice
Simplify each product.
(3x + 4)(x + 3) b. (2x – 5)(x – 2) c. (x – 3)(x + 6)
2. Simplify (6n – 8)( 2𝑛 2 +𝑛+7)
3𝑥 2 +13𝑥+12
2𝑥 2 −9𝑥+10
𝑥 2 +3𝑥−18
12𝑛 3 −10 𝑛 2 +34𝑛−56