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§ 6.2

§ 6.2. Multiplying Polynomials. Product Rule. When multiplying exponential expressions with the same base, add the exponents . A time to add…. Blitzer, Introductory Algebra , 5e – Slide # 2 Section 6.2. Product Rule . Multiply x 3 ·x 5. EXAMPLE.

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§ 6.2

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  1. §6.2 Multiplying Polynomials

  2. Product Rule When multiplying exponential expressions with the same base, add the exponents. A time to add… Blitzer, Introductory Algebra, 5e – Slide #2 Section 6.2

  3. Product Rule Multiply x3·x5 EXAMPLE We used the Product Rule. When multiplying exponential expressions with the same base, add the exponents. Note that the product rule does not apply to exponential expressions with different bases. Blitzer, Introductory Algebra, 5e – Slide #3 Section 6.2

  4. Product Rule Multiply 23·22 EXAMPLE We used the Product Rule. When multiplying exponential expressions with the same base, add the exponents. Note: We do not change the base! Blitzer, Introductory Algebra, 5e – Slide #4 Section 6.2

  5. Power Rule for Exponents The Power Rule When an exponential expression is raised to a power, multiply the exponents. A time to multiply… Blitzer, Introductory Algebra, 5e – Slide #5 Section 6.2

  6. Power Rule for Exponents Find (x2)5 We used the Power Rule. When an exponential expression is raised to a power, multiply the exponents. EXAMPLE Blitzer, Introductory Algebra, 5e – Slide #6 Section 6.2

  7. Power Rule Find (34)2 We used the Power Rule. When an exponential expression is raised to a power, multiply the exponents. Note: We do not change the base! EXAMPLE Blitzer, Introductory Algebra, 5e – Slide #7 Section 6.2

  8. Products to Powers Rule for Exponents When a product is raised to a power, raise each factor to the power. Blitzer, Introductory Algebra, 5e – Slide #8 Section 6.2

  9. Products to Powers Rule for Exponents Find (5x3)2 First, we used the Products to a Power Rule. When a product is raised to a power, raise each factor to the power. Second, we used the Power Rule. When an exponential expression is raised to a power, multiply the exponents. EXAMPLE Products to a Power Rule Power Rule Blitzer, Introductory Algebra, 5e – Slide #9 Section 6.2

  10. Multiplying Monomials To multiply monomials with the same variable base, multiply the coefficients and then multiply the variable parts. Use the product rule for exponents to multiply the variables: Keep the variable and add the exponents. Blitzer, Introductory Algebra, 5e – Slide #10 Section 6.2

  11. Multiplying Monomials Multiply (3x2)(5x7) EXAMPLE Multiply the coefficients and multiply the variables. Add the exponents. Simplify. Blitzer, Introductory Algebra, 5e – Slide #11 Section 6.2

  12. Multiplying a Monomial and a Polynomial To multiply a monomial and a polynomial that is not a monomial, use the distributive property to multiply each term of the polynomial by the monomial. Blitzer, Introductory Algebra, 5e – Slide #12 Section 6.2

  13. Multiplying a Monomial and a Trinomial Multiply 3x(2x2 - 5x + 7) EXAMPLE Use the Distributive Property. Multiply the coefficients and add exponents. Simplify. Blitzer, Introductory Algebra, 5e – Slide #13 Section 6.2

  14. Multiplying Polynomials Multiply each term of one polynomial by each term of the other polynomial. Then combine like terms. For example, if multiplying a binomial by a trinomial – you would have 6 products initially before you combined like terms. Blitzer, Introductory Algebra, 5e – Slide #14 Section 6.2

  15. Multiplication of Polynomials Multiply (3x + 2)(2x – 7) (3x + 2)(2x - 7) = 3x(2x – 7) + 2(2x – 7) = 3x(2x) – 3x(7) + 2(2x) – 2(7) = 6x2 – 21x + 4x – 14 = 6x2 – 17x – 14 Multiply the second binomial by each term of the first binomial. Use the distributive property. Multiply. Note the 4 products here. That’s because 2 times 2 = 4. Simplify. Blitzer, Introductory Algebra, 5e – Slide #15 Section 6.2

  16. Multiplying Polynomials EXAMPLE Multiply SOLUTION Rearrange factors Multiply coefficients and add exponents Simplify Blitzer, Introductory Algebra, 5e – Slide #16 Section 6.2

  17. Multiplying Polynomials EXAMPLE Multiply SOLUTION Distribute Multiply coefficients and add exponents Blitzer, Introductory Algebra, 5e – Slide #17 Section 6.2

  18. Multiplying Polynomials EXAMPLE Note this: We multiply each term of the binomial by each term of the trinomial. We get 6 products in all. Multiply SOLUTION Multiply the trinomial by each term of the binomial Distribute Multiply coefficients and add exponents Simplify Blitzer, Introductory Algebra, 5e – Slide #18 Section 6.2

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