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Multiply polynomials.

Objectives. Multiply polynomials. Use binomial expansion to expand binomial expressions that are raised to positive integer powers. To multiply a polynomial by a monomial, use the Distributive Property and the Properties of Exponents. Example 1: Multiplying a Monomial and a Polynomial.

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Multiply polynomials.

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  1. Objectives Multiply polynomials. Use binomial expansion to expand binomial expressions that are raised to positive integer powers. To multiply a polynomial by a monomial, use the Distributive Property and the Properties of Exponents.

  2. Example 1: Multiplying a Monomial and a Polynomial Find each product. A. 4y2(y2+ 3) 4y2(y2+ 3) 4y2  y2+ 4y2 3 4y4 + 12y2 B. fg(f4 + 2f3g – 3f2g2 + fg3) fg(f4 + 2f3g – 3f2g2 + fg3) fgf4 + fg 2f3g – fg  3f2g2 + fgfg3 f5g + 2f4g2 – 3f3g3 + f2g4

  3. Check It Out! Example 1 Find each product. a. 3cd2(4c2d– 6cd + 14cd2) b. x2y(6y3 + y2 – 28y + 30)

  4. To multiply any two polynomials, use the Distributive Property and multiply each term in the second polynomial by each term in the first. Keep in mind that if one polynomial has m terms and the other has n terms, then the product has mn terms before it is simplified.

  5. Example 2A: Multiplying Polynomials Find the product. (a – 3)(2 – 5a + a2) Method 1 Multiply horizontally. (a – 3)(a2 – 5a + 2) a(a2) + a(–5a)+ a(2) – 3(a2) – 3(–5a) –3(2) a3 – 5a2+ 2a – 3a2 + 15a – 6 a3 – 8a2+ 17a – 6

  6. a2 – 5a + 2 a – 3 Example 2A: Multiplying Polynomials Find the product. (a – 3)(2 – 5a + a2) Method 2 Multiply vertically. – 3a2 + 15a – 6 a3 – 5a2+ 2a a3 – 8a2+ 17a – 6

  7. Check It Out! Example 2a Find the product. Multiply horizontally. (3b – 2c)(3b2 – bc – 2c2)

  8. Check It Out! Example 2b Find the product. Multiply vertically (x2 – 4x + 1)(x2 + 5x – 2)

  9. Find the product. (a + 2b)3

  10. Find the product. (x + 4)4

  11. Find the product. (2x – 1)3

  12. Lesson Quiz Find each product. 1. 5jk(k – 2j) 5jk2– 10j2k 2. (2a3– a + 3)(a2+ 3a – 5) 2a5 + 6a4 – 11a3+ 14a – 15 3. (3a – b)3 27a3 – 27a2b + 9ab2 – b3

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