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10.
h. a(a - b) - b(b - c) - c(c - a)
= a² - ab - b² + bc - c² + ac
= a² - b² - c² - ab + bc + ac

i. 3x(x - 1) - x(x + 1) + 2x(x - 2)
= 3x² - 3x - x² - x + 2x² - 4x
= 4x² - 8x

j. p² + 1/4 p - 3 - p(p - 2) + 2p(3p + 1)
= p² + 1/4 p - 3 - p² + 2p + 6p² + 2p
= 6p² + 4 1/4 p - 3

11.
a. 2(5x + 4) - 3(x - 7)
= 10x + 8 - 3x - 21
= 7x - 13

b. 4(6x - 3) - 5(4x - 5)
= 24x - 12 - 20x + 25
= 4x + 13

c. 2(x - 3) - 4(2x + 1)
= 2x - 6 - 8x - 4
= -6x - 10

d. (2x + 3)/4 - (x - 2)/3
= [3(2x + 3) - 4(x - 2)]/12
= (6x + 9 - 4x + 8)/12
= (2x + 17)/12

e. 2/3 (2x - 5) - 3/4 (-3x + 5)
= 2(2x - 5)/3 - 3(-3x + 5)/4
= (4x - 10)/3 - (-9x + 15)/4
= [4(4x - 10) - 3(-9x + 15)]/12
= (16x - 40 + 27x - 45)/12
= (43x - 85)/12

f. 2(a - 1) + (a + 2) . 3
= 2a - 2 + 3(a + 2)
= 2a - 2 + 3a + 6
= 5a + 4

g. -3(-2x + 5) + 2(-1 + 2x)
= 6x - 15 - 2 + 4x
= 10x - 17

h. 5(-x + 2) + 4(3x - 4)
= -5x + 10 + 12x - 16
= 7x - 6

i. 3(a - 4/3) + 2(a + 1/2)
= 3a - 4 + 2a + 1
= 5a - 3

j. (2x + 1)/2 + (x - 4)/3
= [3(2x + 1) + 2(x - 4)]/6
= (6x + 3 + 2x - 8)/6
= (8x - 5)/6

12.
A = 3x + 1
B = -2x + 3
C = 4x - 5

a. A + B + 2C
= (3x + 1) + (-2x + 3) + 2(4x - 5)
= 3x + 1 - 2x + 3 + 8x - 10
= 9x - 6

b. 2A - 3B + 4C
= 2(3x + 1) - 3(-2x + 3) + 4(4x - 5)
= 6x + 2 + 6x - 9 + 16x - 20
= 28x - 27

c. 2A - {3A - (B - 2C)} - C
= 2(3x + 1) - {3(3x + 1) - [(-2x + 3) - 2(4x - 5)]} - (4x - 5)
= 6x + 2 - {9x + 3 - (-2x + 3 - 8x + 10)} - 4x + 5
= 6x + 2 - {9x + 3 - (-10x + 13)} - 4x + 5
= 6x + 2 - {9x + 3 + 10x - 13} - 4x + 5
= 6x + 2 - (19x - 10) - 4x + 5
= 6x + 2 - 19x + 10 - 4x + 5
= -17x + 17

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