By Ralph S. Underwood, Thomas R. Nelson, Samuel Selby

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2] USEFUL IDENTITIES Illustrative A. 1. 23 Examples Type Products 3(2z - 2 3x 2. (2x + 3t/) 3. (3z 2) 4. (5z - 2 2 + = = 4)(5x = = 1) 2 (2z) 2 (3z) + 4) - 2 3(2z ) 3(3x) 6z2 - Qx 3. + 3-1 = 9z 2 + + - 2(2*) + 2(3z)(2) - 2 == (5x) 42 22 = 25x 2 - - 12* + 4. 16. B. Examples in Factoring 5. 6. 7. - Qax + 2a = 2a(o; - 3z + 1). 4z - 9 = (2x) 2 - 3 = (2x - 3)(2x + 3). 4x + 4az + a - 2 + 2^/6 - 6 - 2y6 + & = (4z + 4ax + a = (2a; + a) - (y - 6) = [(2a; + a) - (y - 6)][(2s + a) + (y = (2x + a - + 6)(2a; + o + y - 6).

C To y sum the of + 2z from 3x -4x 2 + 3xy - 2 over 2x the excess of 4xy + - 2c 56. Subtract 4x 57. 3x 2 2 Sxy + y 2 and + 4xy 5xy - y + 2y Remove 59. 60. 61. 62. -5xy - 65. x + 8x 2 add 6. 7c2 2d and symbols of aggregation and the collect like terms. - 1 - (3x - 1)]. 4 [2x - [-z + (2y - x)]. -[(2x - 3i/ + y] -3(o - 26) + 6{ -4 - [6 - 2(4 + 6)]}. - [(2x - y - 4) - (3y - 2)]. (3x + y + 6) - 2 2 2 ) -3x2 2 7 2 Insert parentheses preceded by a but the first two terms. 63. 2 4. 58. How much must be added to the sum of 3a& + -6 + 3c to give -5a6 - c ?

3a - 2)(2a - 3x 78. (x 80. 82. 1). 5). 84. - 86. 85. -3(2 87. (-3x + y)(y + 3x). 2 2 -5(3x - y)(3x + y). 89. 91. (3 - - 2x)(3 + 2) 93. -3(x 95. -(5x - Note. x)(3x 88. 2 +xy - 2xy + 2 - 2y y - 5)(x + -2(4 94. (lOx 2 by y 2). -(x + 2)(x - 3). - 4). (2a + 3)(a -2(5a l)(3a + 1). - y). (2x + 2/)(2x -(2x - y)(2x + y). 92. 2x). 4j/) 2 90. (2x 2 2 When carried out 1). +y x3 76. y - x2 x [Ch. I 7)(2x - + 2 x)(4 3) + 7). - x). 2 . 96. (4x . the multiplications in problems 77-96 have been the methods given in this chapter, the student should study Arts.

### Intermediate Algebra by Ralph S. Underwood, Thomas R. Nelson, Samuel Selby

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