Question

Which expressions are equivalent to 4d+6+2d

(Choice A) 2(3d+3)
(Choice B) 6(d+6)
(Choice C) (3d+3)+(3d+3)

Answer 1

(Choice A) 2(3d+3) & (Choice C) (3d+3)+(3d+3)

Explanation:

`4D + 6 + 2D = 6D + 6 = 2(3D + 3)` <--- A is correct

`4D + 6 + 2D = 6D + 6 = 6(D +1)` < --- B is NOT correct

`4D + 6 + 2D = 6D + 6 = 3d + 3d + 3 + 3 = (3d + 3)+(3d +3)` by associative and commutative properties

so C is correct

A and C are both correct.

Answer 2

Choices A and C

Explanation:

Start by simplifying the original expression.

4d+6+2d

Combine like terms

6d+6

Now, we can check each expression to see if it is equivalent to 6d+6

Choice A:

2(3d+3)

Distribute the 2

2(3d)+2(3)

6d+6 --> It is equivalent!

Choice B:

6(d+6)

Distribute the 6

6(d)+6(6)

6d+36 --> No, it is not equivalent

Choice C

(3d+3)+(3d+3)

The parentheses aren't necessary so we can take them out.

3d+3+3d+3

Combine like terms

6d+6 --> It is equivalent!