MTH 030 -- Elementary Algebra -- Exercise Solutions
Section:
5.1

22)

 

24)

 

26)

28)

 

30)

 

38)  3x + 6 = 3(x + 2)          Distributive Law

40)  27a2 - 9a +45 = 9(3a2 -a +5)          Distributive Law

42)  b3 -3b2 = b2(b - 3)          Distributive Law

44)  r3 + r2 = r2(r + 1)          Distributive Law

46)  3x2y3 -9x4y3 = 3x2y3(1 - 3x2)          Distributive Law

48)  14xyz - 16x2y2z = 2xyz(7 - 8xy)           Distributive Law

50)  2x - 4y + 8z = 2(x - 2y + 4z)          Distributive Law

 

62)  -x - 2y = (-1)(x + 2y) = -(x + 2y)           Distributive Law

64) -3x + 8z = (-1)(3x - 8z) = -(3x - 8z)           Distributive Law

66)  -3r + 2s -3 = (-1)(3r - 2s + 3) = -(3r - 2s +3)           Distributive Law

68)  -6yz + 12xz - 5xy = (-1)(6yz - 12xz + 5xy) = -(6yz - 12xz + 5xy)            Distributive Law

70)  -4a2 + 6a = -2a(2a - 3)          Distributive Law

72)  -25x4y3 + 30x2y3 = -5x2y3(5x2 - 6)           Distributive Law

74)  -10x4y3z2 + 8x3y2z - 20x2y = -2x2y(5x2y2z2 - 4xyz + 10)          Distributive Law

 

76) bx + bz + 5x + 5z = b(x + z) + 5(x + z) = (b + 5)(x + z)

78)  9p - 9q + mp - mq = 9(p - q) + m(p - q) = (9 + m)(p - q)

80)  pm - pn + qm - qn = p(m - n) + q(m - n) = (p + q)(m - n)

82) 3xy + 3xz -5y - 5z = 3x(y + z) + (-5)(y + z) = 3x (y + z) - 5(y + z) = (3x - 5)(y + z)

84) 3ac + a + 3bc + b = 3ac + 3bc + a + b = 3c(a + b) + (1)(a + b) = (3c + 1)(a + b)

86)  6x2 + 2x + 9x + 3 = 2x(3x + 1) + 3(3x + 1) = (2x + 3)(3x + 1)

88)   ax + bx - a - b = x(a + b) + (-1)(a + b) = (x - 1)(a + b)

90)   2xy - 3y2 + 2x - 3y = y(2x - 3y) + 1(2x - 3y) = (y + 1)(2x - 3y)

92)  2a4 + 2a3 - 4a - 4 = 2a3(a + 1) + (-4)(a + 1) = (2a3 - 4)(a + 1)

94)   x3y2- 2x2y2 + 3xy2 - 6y2 = y2(x3 - 2x2 + 3x - 6) = y2(x2[x - 2] +3[x - 2]) =y2([x2 + 3][x - 2] = y2(x2 + 3)(x - 2)

96)  -4abc - 4ac2 + 2bc + 2c2 = 2c(-2ab -2ac + b + c) = 2c(-2a[b + c] + (1)(b + c)] = 2c([-2a + 1][b + c])

       = 2c(-2a + 1)(b + c) = -2c(2a - 1)(b + c)

98)   2x3z - 4x2z + 32xz - 64z = 2z[x3 - 2x2 + 16x - 32] = 2z[x2(x - 2) + 16(x - 2)] = 2z[(x2 + 16)(x - 2)] = 2z(x2 + 16)(x - 2)