By Bernard Kolman; Arnold Shapiro

ISBN-10: 0124178758

ISBN-13: 9780124178755

ISBN-10: 1483271218

ISBN-13: 9781483271217

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67. 68. + + Compute each of the following. 2 (x -y)(x + y) - x(x + y) (2x - 1)(3x + 2) - (x - 2)(x + 3) x( -x - 3) + ( -x + 4)2 (x - 2)2 - x(x - I ) When a polynomial of degree 3 is multiplied by a polynomial of degree 4, the degree of the product is (a) 12 (b) I (c) 7 (d) � (e) none 3x(yx2 + xy) + xy(x2 - x) (x - l)(x + 3) - x2 2x(x - 3) - 4(x2 - 4) (x + 4)(x - 4) - (x - 2)2 of these. When a polynomial of degree degree of the product is (a) of these. 60. 62. 64. 66. ru 69. 67)2 Im] 70. 39y)2 [IB] 71.

But what can we do with the absolute value of a variable, say lxi? We don't know whether x is positive or negative, so we can't write lxl = x. For instance, when x = -4 we have and when x = lxl = 1 - 41 = 4 # x 4 Ix I = { x if x is 0 or positive 141 = 4 = x We must define absolute value so that it works for both positive and negative values of a variable . lxl = -x if x is negative When x is positive, say x = 4, the absolute value is the number itself; when x is negative, say x = -4, the absolute value is the negative of x or + 4.

Ey) Commutative law of multiplication = (t · ;)y Associative law of multiplication = -21 y (2x - 4) + 7 = [2x + ( -4)] + 7 = 2x + [( -4) + 7] Associative law of addition = 2x + 3 PROGRESS CHECK 3 Use the commutative and associative laws to simplify. (a) 4 + (2x + 2) Answers (a) 6 + 2x (b) (b) 4x (�x}( 12° ) (c) 11 - Jx (c) (5 - 3x) + 6 25 26 THE REAL NUMBER SYSTEM The distributive laws deal with both addition and multiplication. For instance, 2(3 + 4) = 2(7) (1 + 2)5 = (3)5 and We may notice that 2(3) + 2(4) and 1(5) + 2(5) = = = = 14 15 6 + 8 = 14 5 + 10 = 1 5 produce the same results.

### Algebra for college students by Bernard Kolman; Arnold Shapiro

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