This document reviews rules of exponents and introduces multiplying polynomials using the distributive property and box method. It defines monomials, binomials, and trinomials. Examples are provided of distributing a monomial over a binomial using the box method, including rewriting the expression by combining like terms.

1. Multiplying Polynomials I Learning how to multiply a binomial with a monomial

2. Rules of Exponents - Review Before we begin multiplying polynomials let’s review Rules of Exponents

3. The Invisible Exponent When an expression does not have a visible exponent its exponent is understood to be 1.

4. Product of like bases When multiplying two expressions with the same base you add their exponents. For example

5. Power to a Power When raising a power to a power you multiply the exponents For example

6. Product to a Power When you have a product of two or more numbers, you raise each factor to the power For example

7. Quotient with like bases When dividing two expressions with the same base, you subtract the exponents For example

8. Negative Powers When you have negative exponents, flip the term to the other side (top/bottom) of the fraction Examples

9. Zero Power Rule Anything to the zero power (except 0) is 1

10. Classifying Polynomials POLYNOMIALS MONOMIALS (1 TERM) BINOMIALS (2 TERMS) TRINOMIALS (3 TERMS) x 2 + 4x x 2 x 2 + 4x - 4

11. 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

12. Distributive Property (Box Method) -7(5x + 8) = -35x – 56 Ex. 1 5x + 8 -7 -35x -56 x(x + 4) = x 2 + 4x Ex. 2 x + 4 x x 2 4x

13. Distributive Property (Box Method) 2x(x - 6) = 2x 2 – 12x Ex. 3 x - 6 2x 2x 2 -12x 3h 2 (5h - 9) = 15h 3 – 27h 2 Ex. 4 5h - 9 3h 2 15h 3 -27h 2

14. Distributive Property (Box Method) 9p 3 (2p 5 + 6p) = 18p 8 + 54p 4 Ex. 5 2p 5 +6p 9p 3 18p 8 +54p 4 7k(k 9 – 6k) = 7k 10 – 42k 2 Ex. 6 k 9 - 6k 7k 7k 10 -42k 2

15. Questions