January 18, 2017 Lesson 5.5 Multiplying Polynomials; Special Products We have already learned how to multiply two monomials such as = To multiply a polynomial by a monomial, use the distributive property to multiply each term in the polynomial by the monomial. 6 4 6x - 15x + 21x 2 Now try these! 4 5 36x - 28x + 12x 5 3 3 4 4 3 4 5 5 -15x yz + 12x y z - 24x y z 3 2 3 2 3 15x - 40x - 6x + 14x = 9x - 26x 2 . 1 January 18, 2017 To multiply two polynomials, multiply each term in the second polynomial by each term in the first polynomial. Then combine like terms. We can multiply two binomials together using the distributive property twice. First distribute 5x over (2x - 9) then distribute 1 over (2x - 9). 2 10x - 45x + 2x - 9 2 10x - 43x - 9 . 2 January 18, 2017 Now try these on your own! 2 = x + 8x - 5x - 40 2 = x + 3x - 40 FO 2 = 12x - 30x - 14x + 35 2 = 12x - 44x + 35 I L 2 2 = 3x + 7xy + 12xy + 28y 2 2 = 3x + 19xy + 28y F O I L i r s t u t t e r n n e r a s t Multiplying a binomial and trinomial. We distribute each term in the binomial over each term in the trinomial and simplify the result. 2 2 3 = x - 5x + 4x - 3x + 15x - 12 3 2 = x - 8x + 19x - 12 . 3 January 18, 2017 Try these on your own! 3 2 2 = 12x + 4x - 8x - 15x - 5x + 10 3 2 = 12x - 11x - 13x + 10 4 3 2 3 2 2 = x + 4x - 2x + 7x + 28x - 14x + 5x + 20x - 10 4 3 2 = x + 11x + 31x + 6x - 10 You may find it easier to multiply this last problem vertically. . 4 January 18, 2017 Consider Binomials that differ only in the sign separating the terms are called conjugates: a + b and a - b are conjugates. The product of conjugates results in a difference of two perfect squares. For example: 2 2 2 (5x) - (3) = 25x - 9 Try these on your own! 2 x - 36 2 4y - 49 2 2 16x - 81y . 5 January 18, 2017 Squaring a Binomial If a and b are real numbers, variables, or expressions, then , and For example: Try these yourself. 2 9x + 24x + 16 2 4y - 44y + 121 49 - 42z + 9z 2 . 6 January 18, 2017 Lesson 5.5 pages 387-388. 7 January 18, 2017 108) r r-2 109) 8

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