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# Multiplying Polynomials I

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### Transcript

• 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