Question

Is -2/3(12b - 6 + 9b - 18) equivalent to 2b(b + 8)? Show your work.

Answer 1

This is NOT equivalent to 2b(b + 8).

Explanation:

Start with -2/3(12b - 6 + 9b - 18). Simplify this. First, combine the like terms inside the set of parentheses:

(-2/3)(21b - 24)

Simplify this by applying the distributation property of multiplication:

-14b + 16

Finally, factor out 2: 2(-7b + 8)

This is NOT equivalent to 2b(b + 8).

Answer 2

No, they are not equivalent

Explanation:

`(-2)/(3)(12b - 6 + 9b - 18) = (-2)/(3)(12b + 9b - 6 - 18)\\\\=(-2)/(3)(21b - 24)\\\\ = (-2)/(3)*21b -24*(-2)/(3)\\\\= -2*7b + 8*2\\\\= 2( -7b + 8)`