There are three techniques you can use for multiplying polynomials.

The best part about it is that they are all the same! Huh? Whaddaya mean?

It’s all about how you write it…Here they are!1)Distributive Property(ALWAYS WORKS)

2)Stacking3)FOIL binomials only

Sit back, relax (but make sure to write this down), and I’ll show ya!

1) Simplify: 5(7n - 2)

5 • 7n

35n - 10

Multiplying

- 5 • 2

Use the distributive property.

3(8 12)

4a a 2) Simplify:

6a2 + 9a

3) Simplify: 6rs(r2s - 3) 6rs • r2s

6r3s2 - 18rs

38

4a a

312

4a

- 6rs • 3

4) Simplify: 4t2(3t2 + 2t - 5)

12t4 + 8t3 - 20t2

5) Simplify: - 4m3(-3m - 6n + 4p)

(x-3)(2x-4)

F : Multiply the First term in each binomial. 2x • 4x = 8x2

There is an acronym to help us remember how to multiply two BINOMIALS without stacking them.

F.O.I.L.

(2x + -3)(4x + 5)

(2x + -3)(4x + 5) = 8x2 + 10x + -12x + -15 = 8x2 + -2x + -15

O : Multiply the Outer terms in the binomials. 2x • 5 = 10x

I : Multiply the Inner terms in the binomials. -3 • 4x = -12x

L : Multiply the Last term in each binomial. -3 • 5 = -15

Multiply

1) (3a + 4)(2a + 1) = 6a2 = 6a2 + 11a + 4 + 3a + 8a + 4

2) (x + 4)(x – 5)

5) Multiply (2x - 5)(x2 - 5x + 4)You cannot use FOIL because they are not BOTH binomials. You must use the

distributive property.

2x(x2 - 5x + 4) - 5(x2 - 5x + 4)

2x3 - 10x2 + 8x - 5x2 + 25x - 20

Group and combine like terms.

2x3 - 10x2 - 5x2 + 8x + 25x - 20

2x3 - 15x2 + 33x - 20