Question

Factor Linear Expressions Quick Check
3 of 53 of 5 Items
Question
Rewrite the expression 2a3b+6a2b2
by factoring out the GCF.(1 point)
Responses

2a2b(ab+3ab)
2 a superscript 2 baseline b left parenthesis a b plus 3 a b right parenthesis

2a2(ab+3b)
2 a superscript 2 baseline left parenthesis a b plus 3 b right parenthesis

2a2(a+3b)
2 a superscript 2 baseline left parenthesis a plus 3 b right parenthesis

2a2b(a+3b)

Answer 1

To factor the expression \( 2a^3b + 6a^2b^2 \), we first need to identify the greatest common factor (GCF) of the two terms.

1. The coefficients are 2 and 6; the GCF of these is 2.
2. For the variable \( a \), \( a^3 \) and \( a^2 \): the GCF is \( a^2 \).
3. For the variable \( b \), \( b \) and \( b^2 \): the GCF is \( b \).

Combining these, the overall GCF is \( 2a^2b \).

Now, we factor \( 2a^2b \) out of the expression:

\[
2a^3b + 6a^2b^2 = 2a^2b(a + 3b)
\]

Thus, the correct factorization is:

\[
2a^2b(a + 3b)
\]

Therefore, the correct response is:

**2a^2b(a + 3b)**.