Algebra & Trigonometry by Cynthia Y. Young

By Cynthia Y. Young

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Recognize like terms. Learn formulas for special products. Adding and Subtracting Polynomials Polynomials in Standard Form The expressions 3x2 Ϫ 7x Ϫ 1 4y3 Ϫ y 5z are all examples of polynomials in one variable. A monomial in one variable, ax k, is the product of a constant and a variable raised to a nonnegative-integer power. The constant a is called the coefficient of the monomial, and k is called the degree of the monomial. A polynomial is the sum of monomials. The monomials that are part of a polynomial are called terms.

8Ϫ2 18. 5 # 2Ϫ4 # 32 4. (Ϫ4)2 9. 90 14. 3Ϫ4 19. Ϫ6 # 3Ϫ2 # 81 5. Ϫ52 10. Ϫ8x0 15. Ϫ6 # 52 20. qxd 8/7/12 26 5:34 PM Page 26 C H A P T E R 0 Prerequisites and Review In Exercises 21–50, simplify and write the resulting expression with only positive exponents. 21. x2 # x3 22. y3 # y5 23. x2 xϪ3 24. y3 # yϪ7 25. (x2 ) 26. (y3)2 27. (4a)3 28. (4x2) 29. (Ϫ2t)3 30. (Ϫ3b)4 31. (5xy2) (3x3y) 3 33. x5 y3 34. 7 xy b -4 37. a b 2 41. 2 45. 42. y5 x2 35. -2 -5 y x (2xy)2 (- 2xy) Ϫ2 y-4 x5 46. 4 3 a2(- xy4) 4 (2x3) (y-1z) 3 2t x4(- a3 y2) 4 5 50.

Example 7 illustrates the difference of two squares and perfect squares. EXAMPLE 7 Find the following: Multiplying Binomials Resulting in Special Products a. (x Ϫ 5)(x ϩ 5) b. (x ϩ 5)2 c. (x Ϫ 5)2 Inner r Difference of two squares a. (x - 5)(x + 5) = x + 5x - 5x - 5 = 2 2 r r Outer Last s First r Solution: x2 - 52 = x2 - 25 Inner r r First b. (x + 5) = (x + 5)(x + 5) = x + 5x + 5x + 52 = x2 + 2(5x) + 52 = x2 + 10x + 25 2 2 r r Last Outer Inner r r First r r c. (x - 5)2 = (x - 5)(x - 5) = x2 - 5x - 5x + 52 = x2 - 2(5x) + 52 = x2 - 10x + 25 Outer Last Let a and b be any real number, variable, or algebraic expression in the following special products.

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