1. Ch. 12-4 Part 1 Multiplying Polynomials
~Multiply Coefficients and add exponents of like bases.
Example 1: Multiply the following monomials.
a.) (4a3)(-5a2) b.) (2y4)(4y)
-20a5
8y5
Example 2: Multiply the following monomials.
a.) (-3x3)(2x5) b.) (x2)(16x)
-6x8
16x3

2. We know that 5(3 + 4) = 5(3) + 5(4) = 15 + 20 = 35
Now that you can multiply monomials, you can put the distributive property to work.
We know that 5(3 + 4) = 5(3) + 5(4) = = 35
In the same way 5(3x + 4y) = 5(3x) + 5(4y) = 15x + 20y
Example 3: Multiply each monomial by each binomial.
a.) 3x(2x + 8) b.) 2x(x + 4y)
c.) –y2(2y + 7) d.) -2d3(d2 – 1)
6x2 + 24x
2x2 + 8xy
-2y3 – 7y2
-2d5 + 2d3

3. Ch. 12-4 Part 2 Multiplying Polynomials
You have learned to use the distributive axiom to multiply a polynomial
by a monomial:
(4x + 3)(3x) = 12x2 + 9x
If you replace 3x in the example above by the polynomial 3x + 4,
the distributive axiom can still be applied:
(4x+ 3)(3x + 4)
An easy way to multiply polynomials is called using the FOIL method.
FOIL
First Outer Inner Last

4. FOIL OR Box Method First Outer Inner Last (4x + 3)(3x + 4) 4x 3 3x 4
First: 4x(3x) = 12x2
(4x + 3)(3x + 4)
Outer: 4x(4) = 16x
Inner
Outer
Inner: 3(3x) = 9x
Last: 3(4) = 12 OR
Then rewrite the problem:
Box Method
12x2 + 9x + 16x + 12 4x 3 3x 4
Then simplify any like terms
12x2 + 25x + 12
12x2 9x
16x 12

5. Example 1: Multiply the following binomials.
a.) (2x + 1)(3x + 2) b.) (x + 1)(2x + 5)
c.) (3x + 4)(2x – 1) d.) (2x – 2)(x – 3)
6x2 + 7x + 2
2x2 + 7x + 5
6x2 + 5x - 4
2x2 – 8x + 6