Rewrite the expression 2a3b+6a2b2

Question

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

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

The GCF of the coefficients (2 and 6) is 2.

For the variables:

• The GCF of \( a^3 \) and \( a^2 \) is \( a^2 \).
• The GCF of \( b \) and \( b^2 \) is \( b \).

Therefore, the GCF of the entire expression is \( 2a^2b \).

Now, we can factor out \( 2a^2b \) from the original expression:

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

So, the correct rewritten expression by factoring out the GCF is:

2a^2b(a + 3b)