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# Multiplying Polynomials I

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### Multiplying Polynomials I

1. 1. Multiplying Polynomials I Learning how to multiply a binomial with a monomial
2. 2. Rules of Exponents - Review <ul><li>Before we begin multiplying polynomials let’s review Rules of Exponents </li></ul>
3. 3. The Invisible Exponent <ul><li>When an expression does not have a visible exponent its exponent is understood to be 1. </li></ul>
4. 4. Product of like bases <ul><li>When multiplying two expressions with the same base you add their exponents. </li></ul><ul><li>For example </li></ul>
5. 5. Power to a Power <ul><li>When raising a power to a power you multiply the exponents </li></ul><ul><li>For example </li></ul>
6. 6. Product to a Power <ul><li>When you have a product of two or more numbers, you raise each factor to the power </li></ul><ul><li>For example </li></ul>
7. 7. Quotient with like bases <ul><li>When dividing two expressions with the same base, you subtract the exponents </li></ul><ul><li>For example </li></ul>
8. 8. Negative Powers <ul><li>When you have negative exponents, flip the term to the other side (top/bottom) of the fraction </li></ul><ul><li>Examples </li></ul>
9. 9. Zero Power Rule <ul><li>Anything to the zero power (except 0) is 1 </li></ul>
10. 10. Classifying Polynomials POLYNOMIALS MONOMIALS (1 TERM) BINOMIALS (2 TERMS) TRINOMIALS (3 TERMS) x 2 + 4x x 2 x 2 + 4x - 4
11. 11. The Distributive Property - Back with a Vengeance <ul><li>We will be applying the Distributive Property to multiply polynomials </li></ul><ul><li>You will learn the box method for distribution </li></ul>
12. 12. Distributive Property (Box Method) <ul><li>-7(5x + 8) </li></ul>= -35x – 56 Ex. 1 5x + 8 -7 -35x -56 x(x + 4) = x 2 + 4x Ex. 2 x + 4 x x 2 4x
13. 13. Distributive Property (Box Method) <ul><li>2x(x - 6) </li></ul>= 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. 14. Distributive Property (Box Method) <ul><li>9p 3 (2p 5 + 6p) </li></ul>= 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. 15. Questions