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# COT.Multiplying-Polynomials .pptx

math lesson

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### COT.Multiplying-Polynomials .pptx

1. 1.  Derive the laws of exponent (related to multiplication of polynomials)  Multiply Polynomials
2. 2. Identify what do you call each of the following: exponent base Power
3. 3. Laws of Exponent (for Multiplication) #1: The Product Law: If you are multiplying powers with the same base, KEEP the BASE & ADD the EXPONENTS! So, I get it! When you multiply powers, you add the exponents! 𝒂𝟐 · 𝒂𝟑 = 𝒂𝟐+𝟑 = 𝒂𝟓 𝟐𝟐 · 𝟐𝟑 = 𝟐𝟐+𝟑 = 𝟐𝟓 = 𝟑𝟐
4. 4. Try This: Solutions:
5. 5. #2: Power of a Power Law: If you are raising a power to an exponent, you multiply the exponents! (𝒂𝒎 )𝒏 = 𝒂𝒎𝒏 (𝟐𝟐)𝟑 = 𝟐𝟐∙𝟑 = 𝟐𝟔
6. 6. #3: Product Law of Exponents: If the product of the bases is powered by the same exponent, then the result is a multiplication of individual factors of the product, each powered by the given exponent. (𝒂𝒎 ∙ 𝒃𝒏 )𝒙 = 𝒂𝒎𝒙 𝒃𝒏𝒙 (𝒂𝟐 ∙ 𝒃𝟑 )𝟒 = 𝒂(𝟐)(𝟒) ∙ 𝒃 𝟑 𝟒 = 𝑎8 𝑏12 (𝟒𝒂𝟑)𝟐 = 𝟒(𝟏)(𝟐) ∙ 𝒂(𝟑)(𝟐) = 𝟒𝟐 𝒂𝟔 = 𝟏𝟔𝒂𝟔
7. 7. Try This: Solutions:
8. 8. #4: Zero Law of Exponents: Any base powered by zero exponent equals one. 𝒂𝟎 = 𝟏 𝟐𝟎 = 𝟏 −𝟐𝟎 = −𝟏 (−𝟐)𝟎 = 𝟏
9. 9. Try This: Solutions:
10. 10. Multiplying Polynomials  To multiply monomials and polynomials, you will use some of the properties of exponents that you learned earlier 1. Multiplying Monomial by a Monomial To multiply a monomial with another monomial, multiply the numerical coefficients by applying basic laws of exponent. A. (6y3)(3y5) (6y3)(3y5) 18y8 B. (-3mn2) (9m2n) (-3mn2)(9m2n) -27m3n3
11. 11. B. Multiplying Polynomials To multiply a polynomial by a monomial, use the Distributive Property. 2. Multiplying Monomial by a Polynomial A. 6pq(2p – q) (6pq)(2p – q) Distribute 6pq (6pq)2p + (6pq)(–q) Group like bases together. 12p2q – 6pq2 x y ( ) + 2 2 6 1 2 xy y x 8 2 x y x y ( ) ( )    + 2 2 1 6 2 8 xy x y 2 2    1 2       3x3y2 + 4x4y3
12. 12. It’s Your turn… b. 2(4x2 + x) c. 5r2s2(r – 3s) d. 3a(2a + 4ab) a. (2t)(5t3)
13. 13. Let’s Sum It Up! What are the different Laws of exponent for Multiplication? How do we multiply Polynomials?