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Multiplying Polynomials ILearning how to multiply a binomial with a monomial
Rules of Exponents - Review
Before we begin multiplying polynomials let’s review Rules of Exponents
The Invisible Exponent
When an expression does not have a visible exponent its exponent is understood to be 1.
1xx
Product of like bases
When multiplying two expressions with the same base you add their exponents.
For example
mn bb mnb
42 xx 42x6x
Power to a Power
When raising a power to a power you multiply the exponents
For example
mnb )( mnb
42 )(x 42x 8x
Product to a Power
When you have a product of two or more numbers, you raise each factor to the power
For example
mab)( mmba4)4( x 44 *4 x 4256x
Quotient with like bases
When dividing two expressions with the same base, you subtract the exponents
For example
nmm
na
a
a
5
3x
x35x 2x
Negative Powers
When you have negative exponents, flip the term to the other side (top/bottom) of the fraction
Examples
2x 2
1
z2
1
x2z
Zero Power Rule
Anything to the zero power (except 0) is 1
0p 1 025 1 0000,000,1 1303 yxz ))(1)(( 33 yz 33yz
zab
zba4
249
zba 08 za8
Classifying Polynomials
POLYNOMIALS
MONOMIALS
(1 TERM)
BINOMIALS
(2 TERMS)
TRINOMIALS
(3 TERMS)
x2 + 4xx2 x2 + 4x - 4
The Distributive Property - Back with a Vengeance
We will be applying the Distributive Property to multiply polynomials
You will learn the box method for distribution
Distributive Property (Box Method)
-7(5x + 8)
= -35x – 56
Ex. 1
5x + 8
-7 -35x -56
x(x + 4)
= x2 + 4x
Ex. 2
x + 4
x x2 4x
Distributive Property (Box Method)
2x(x - 6)
= 2x2 – 12x
Ex. 3
x - 6
2x 2x2 -12x
3h2(5h - 9)
= 15h3 – 27h2
Ex. 4
5h - 9
3h2 15h3 -27h2
Distributive Property (Box Method)
9p3(2p5 + 6p)
= 18p8 + 54p4
Ex. 5
2p5 +6p
9p3 18p8 +54p4
7k(k9 – 6k)
= 7k10 – 42k2
Ex. 6
k9 - 6k
7k 7k10 -42k2
Questions