Question

factor $24m - 12p + 72$ to identify the equivalent expressions. choose 2 answers: a $6(4m + 2p + 12)$ b $2(12m - 6p + 36)$ c $12(2m - p + 6)$ d $24(m - 12p + 3)$

Explanation:

Step1: Check Option A

Expand $6(4m + 2p + 12)$:
$6\times4m + 6\times2p + 6\times12 = 24m + 12p + 72$
This does not match $24m - 12p + 72$.

Step2: Check Option B

Expand $2(12m - 6p + 36)$:
$2\times12m - 2\times6p + 2\times36 = 24m - 12p + 72$
This matches the original expression.

Step3: Check Option C

Expand $12(2m - p + 6)$:
$12\times2m - 12\times p + 12\times6 = 24m - 12p + 72$
This matches the original expression.

Step4: Check Option D

Expand $24(m - 12p + 3)$:
$24\times m - 24\times12p + 24\times3 = 24m - 288p + 72$
This does not match $24m - 12p + 72$.

Answer:

B. $2(12m - 6p + 36)$
C. $12(2m - p + 6)$