Simplifying and Factoring Algebraic Expressions

If P = (2a + 3) and Q = (4 - 3a), then what is the value of (P - Q)²?

• 4a² - 6a + 12

• 25a² - 10a + 12

• 25a² - 10a + 1

• 6a² - 6a + 12

Answer explanation

If P = (2a + 3) and Q = (4 - 3a) then, P - Q = (2a + 3) - (4 - 3a) = 2a + 3 - 4 + 3a = (5a -1) So, (P - Q)² = (5a -1)² Using (x - y)² = x² - 2xy + y² (P - Q)² = (5a)² - 2 (5a) (1) + (1)² = 5²a² - 10a + 1 = 25a² - 10a + 1 So, option 3 is correct.

Factor the expression:

4w - 16

• 2(2w - 8)

• 4(w - 16)

• 2(2w - 4)

• 4(w - 4)

Factor 7x(9x -2)-1(9x -2)

• (7x - 1)(9x - 2)

• (7x + 1)(9x - 2)

• (7x - 1)(9x + 1)

• (7x - 2)(9x - 1)

Factor the expression: 8x + 64

• 4(2x -24)

• 2(4x + 30)

• 8(1x - 8)

• 8( x + 8)

Factor the expression using the GCF:
24k + 32

• 8(3k + 4)

• 2(12k + 16)

• 24k + 32

• 8(3k + 5)

Factor

14y - 20

• 7(2y - 3)

• 2(7y -10)

• 14(y-20)

Which expression is equivalent to 22 + 12 after factoring out a common factor?

• 2 x (22 + 6)

• 22 x (1 + 12)

• 2 x (22 + 12)

• 2 x (11 + 6)

Factor completely.

• -4(n - 2)

• 4(n + 2)

• 4(n - 2)

• none of these

Which expression is the completely factored form of 12a - 36?

• 3(4a - 12)

• 6(2a - 6)

• 2(6a - 18)

• 12(a - 3)

• None of the Above