Question

factor $72y + 108z$ to identify the equivalent expressions. choose 2 answers: a $9(7y + 12z)$ b $36(2y + 3z)$ c $6(18y + 12z)$ d $12(6y + 9z)$

Explanation:

Step1: Find GCF of 72 and 108

The greatest common factor (GCF) of 72 and 108 is 36.

Step2: Factor out GCF from original expression

$72y + 108z = 36(2y + 3z)$

Step3: Check other valid factors

We can also use a factor of 12: $12 \times 6 = 72$, $12 \times 9 = 108$, so $72y + 108z = 12(6y + 9z)$

Step4: Verify incorrect options

For option A: $9(7y+12z)=63y+108z
eq 72y+108z$
For option C: $6(18y+12z)=108y+72z
eq 72y+108z$

Answer:

B. $36(2y + 3z)$
D. $12(6y + 9z)$