By Ralph S. Underwood, Thomas R. Nelson, Samuel Selby
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Additional resources for Intermediate Algebra
2 59. 2 . 3. Factoring The a trinomial identities (x (1) + a)(x + 6) 6) (ex + d) = x2 = acx 2 + (a + 6)x (ad + + 06, and (ox (2) + + 6c)x + bd are not worth memorizing in themselves; but they suggest a practical method of multiplying two monomials and thereby aid in the factoring of a trinomial. To illustrate, we may find the product (2x 3)(3x 2) mentally by use of the follow- + ing scheme. The and The 6x 2 The first term of the product is = 2 Go; (2x)(3x) " second term is the sum of the products of "inside terms "outside terms/' or 3(3x) 4x = 5x.
3x + y)(x* -xy + y*). - 3ab + 6 (3a + 6)(9a - Qmp + 9m p (2p + 3mp)(4p -(7/-a)(2/ + ar/ + a -3(2a - 6)(4a + lab + 6 Prove the identity (a + 6 + c) = )]. 25. (x 26. 27. 28. 29. 30. 2ac + 2 2 ). 4 2 2 3 2 ). 2 2 ). 2 2 ). 2 26c both member in the by form + b) + 31. State the identity in + b + c + 2ab + 2 2 and by writing the direct multiplication [(a a2 left 2 c] . problem 30 a suitable form for oral in problems. Use the statement obtained in problem 31 to find the squares indi- cated in problems 32-34.
71x 8 2 30. + - + 4xV + 4y 9a + 6a + 9x - Qx yz + j/V. 28. x . 2 3 x + 8. +a 45. 6 50. x 6 48. - y = (a + 2 06 6) (a + 6 2 ); + m - 27. - l) (2x 3 s 46. 49. 8. ay + 64. 27y + (a + 2h) 3 3 . 6 . HINT. First treat as difference of squares. Factor as a difference of two squares by adding and subtracting a perfect square. 51. x4 54. 55. x4 + 52. x4 64. - + 16. - 12xV + 16tA 4 x 24x 2 + 4y. HINT, x 4 53. x 4 - 24x 2 56. a 4 = + 16 - 10a262 +xy + (x 2 2 + - 2 2 4) 1664 - y'. I6x2 . Factor completely, using the type forms given in this chapter.