By Cynthia Y. Young

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2 # 42 2. 53 7. Ϫ22 # 4 12. aϪ1 17. 8 # 2Ϫ3 # 5 3. (Ϫ3)5 8. Ϫ32 # 5 13. 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.

When the binomials are of the form (ax ϩ b)(cx ϩ d), the outer and inner terms will be like terms and can be combined. W OR DS M ATH Apply the distributive property. (5x Ϫ 1)(2x ϩ 3) ϭ 5x(2x ϩ 3) Ϫ 1(2x ϩ 3) Apply the distributive property. ϭ 5x(2x) ϩ 5x(3) Ϫ 1(2x) Ϫ 1(3) Multiply each set of monomials. ϭ 10x2 ϩ 15x Ϫ 2x Ϫ 3 Combine like terms. ϭ 10x2 ϩ 13x Ϫ 3 Product of First Terms First Inner ᭢ ᭢ ᭢ ᭢᭢ ᭢ (5x Ϫ 1)(2x ϩ 3) ϭ 10x2 ϩ 15x Ϫ 2x Ϫ 3 ᭢ ᭢ ᭢ ᭢ ᭢ The FOIL method ﬁnds the products of the First terms, Outer terms, Inner terms, and Last terms.

YO U R T U R N Multiply (2x Ϫ 3)(5x Ϫ 2). qxd 32 8/3/12 11:17 AM Page 32 C H A P T E R 0 Prerequisites and Review Some products of binomials occur frequently in algebra and are given special names. 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.