Question

Select all expressions that are equivalent to 4(y + 2).

A 4y + 2
B4y + 8
Cy+y + y + y +2
D 5(y +2) – (y + 2)
Ey + y + y + y + 2+2+2+2
F.5(y + 2) - (y – 2)

Answer 1

• B
• D
• E

Explanation:

× A = 4y + 2 = 2(4y/2 + 2/2) = 2(2y + 1) ≠ 4(y + 2)

✓ B = 4y + 8 = 4(4y/4 + 8/4) = 4(y + 2) = 4(y + 2)

× C = y + y + y + y + 2 =

y (1 + 1 + 1 + 1) + 2 = 4y + 2 = A ≠ 4(y + 2)

✓ D = 5(y + 2) – (y + 2) = 5(y + 2) – 1(y + 2) =

(5 – 1)(y + 2) = 4(y + 2)

✓ E = y + y + y + y + 2 + 2 + 2 + 2 =

y (1 + 1 + 1 + 1) + (2 + 2 + 2 + 2) =

4y + 8 = B = 4(y + 2)

× F = 5(y + 2) – (y – 2) =

(5y + 10) + (-y + 2) =

(5y – y) + (10 + 2) =

4y + 12 = 4(y + 3) ≠ 4(y + 2)