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Chapter 6

6-5 Multiplying Polynomials. Chapter 6 . Multiply polynomials. Objectives. To multiply monomials and polynomials, you will use some of the properties of exponents that you learned earlier in this chapter. Multiplying Polynomials. Multiply. A. (6y 3 )(3y 5 ) Solution:

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Chapter 6

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  1. 6-5 Multiplying Polynomials Chapter 6

  2. Multiply polynomials. Objectives

  3. To multiply monomials and polynomials, you will use some of the properties of exponents that you learned earlier in this chapter. Multiplying Polynomials

  4. Multiply. A. (6y3)(3y5) Solution: (6y3)(3y5) Group factors with like bases together. (6 *3)(y3* y5) Multiply. 18y8 Example 1: Multiplying Monomials

  5. B. (3mn2) (9m2n) Solution: (3mn2)(9m2n) Group factors with like bases together. (3 *9)(m * m2)(n2 n)Multiply 27m3n3 Example#1

  6. Multiply Solution: Example#1 (st) (-12 s t2) s2 t2 1 4

  7. a. (3x3)(6x2) Solution: 18x5 b. (2r2t)(5t3) Solution:10r2t4 Check it out!

  8. To multiply a polynomial by a monomial, use the Distributive Property. Multiplying polynomials by Monomials

  9. Distribute 4. Multiply. 4(3x2 + 4x – 8) sol: 4(3x2 + 4x – 8) (4)3x2 +(4)4x – (4)8 multiply 12x2 + 16x – 32 Example 2A: Multiplying a Polynomial by a Monomial

  10. Distribute 6pq. Multiply. 6pq(2p – q) Sol: (6pq)(2p – q) (6pq)2p + (6pq)(–q) 6  2)(p  p)(q) + (–1)(6)(p)(q  q) 12p2q – 6pq2 Example 2B: Multiplying a Polynomial by a Monomial

  11. Multiply a. 2(4x2 + x + 3) Sol: 8x2 + 2x + 6 b. 3ab(5a2 + b) Sol:15a3b + 3ab2 Check it out!

  12. Distribute. Distribute again. To multiply a binomial by a binomial, you can apply the Distributive Property more than once: • (x + 3)(x + 2) = x(x + 2)+ 3(x + 2) • x(x + 2) + 3(x + 2) • x(x) + x(2) + 3(x) + 3(2) Multiply • x2 + 2x + 3x + 6 combine • x2 + 5x + 6 Multiplying Binomials by Binomials

  13. 1. Multiply the First terms. (x+ 3)(x+ 2) x x= x2 2. Multiply the Outer terms. (x+ 3)(x+ 2) x 2= 2x  3. Multiply the Inner terms. (x+ 3)(x+ 2) 3x= 3x   4. Multiply the Last terms. (x+ 3)(x+ 2) 32= 6 (x + 3)(x + 2) = x2+2x + 3x +6 = x2 + 5x + 6 F O I L Another method for multiplying binomials is called : FOIL Method Multiplying Binomial by Binomial

  14. Multiply. (s + 4)(s – 2) Solution: Example s2 + 2s –8

  15. Multiply (x – 4)2 Solution: Example 3B: Multiplying Binomials x2 – 8x + 16

  16. Multiply (8m2 – n)(m2 – 3n) Solution:8m4 – 25m2n + 3n2 Example 3C: Multiplying Binomials

  17. Multiply (a + 3)(a – 4) Solution: Check It Out! Example 3a a2 – a – 12

  18. To multiply polynomials with more than two terms, you can use the Distributive Property several times. Multiply (5x + 3) by (2x2 + 10x – 6): Multiplying POlynomials

  19. (5x + 3)(2x2 + 10x– 6) = 5x(2x2 + 10x –6) + 3(2x2 + 10x– 6) Solution = 5x(2x2 + 10x –6) + 3(2x2 + 10x– 6) = 5x(2x2) + 5x(10x) + 5x(–6) + 3(2x2) + 3(10x) + 3(–6) = 10x3 + 50x2–30x + 6x2 + 30x– 18 = 10x3 + 56x2– 18

  20. –6 2x2 +10x 5x 10x3 50x2 –30x –18 +3 6x2 30x You can also use a rectangle model to multiply polynomials with more than two terms. This is similar to finding the area of a rectangle with length (2x2 + 10x – 6) and width (5x + 3): Box Method Write the product of the monomials in each row and column:

  21. To find the product, add all of the terms inside the rectangle by combining like terms and simplifying if necessary. BoX Method 10x3+ 6x2 + 50x2+ 30x – 30x– 18 10x3+ 56x2– 18

  22. Multiply S0l: Example 4A: Multiplying Polynomials (x – 5)(x2 + 4x – 6) x3 – x2 – 26x + 30

  23. Multiply (2x – 5)(–4x2 – 10x + 3) Sol: Example 4B: Multiplying Polynomials –8x3+ 56x – 15

  24. Multiply (3x + 1)(x3 + 4x2 – 7) Check It Out!!!

  25. The width of a rectangular prism is 3 feet less than the height, and the length of the prism is 4 feet more than the height. a. Write a polynomial that represents the area of the base of the prism. Sol: Application The area is represented by h2 + h– 12.

  26. b. Find the area of the base when the height is 5 ft. Sol: Continue The area is 18 square feet.

  27. DO Problems 1,2,4,13,16,23 and 25 in your book page 427 Student Guided Practice

  28. Do problems 27,30,39,42,45,54,57,60 and 62 in your book page 427 Homework

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