Question

Melissa says the GCF of 8x2y + 4xy is 4. Adam says the GCF is 4y. Erica says the GCF is 4xy. Who is correct? In complete sentences explain your answer, and factor the expression.

Answer 1

Answer:

Erica

Step-by-step explanation:

The given expression is $8x^2y+4xy$.

The prime factorization of the first term is

$8x^2y=2^3\cdot x^2\cdot y$

The prime factorization of the second term is

$4xy=2^2\cdot x\cdot y$

The greatest common factor is product of the least powers of the common factors.

$GCF=2^2\cdot x\cdot y=4xy$

Therefore Erica  is correct.