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

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

2a2(a+3b)

Answer 1

To factor the expression \(2a^3b + 6a^2b^2\) by finding the greatest common factor (GCF):

1. Identify the GCF of the terms:
   • The coefficients are 2 and 6, and their GCF is 2.
   • The variable part for \(a\) is \(a^2\) (the smallest power of \(a\) in both terms).
   • The variable part for \(b\) is \(b\) (the smallest power of \(b\) in both terms).

Thus, the GCF is \(2a^2b\).

2. Now, divide each term by the GCF:

   • The first term: \(2a^3b \div 2a^2b = a\)
   • The second term: \(6a^2b^2 \div 2a^2b = 3b\)

3. Rewrite the expression using the GCF: \[ 2a^3b + 6a^2b^2 = 2a^2b(a + 3b) \]

Therefore, the expression can be factored as: \[ 2a^2b(a + 3b) \]

The correct response is: 2 a superscript 2 baseline b left parenthesis a plus 3 b right parenthesis.