How would you rewrite the expression 18x3y4+12x5y2

Question

by factoring out the GCF?(1 point)
Responses

6x3y2(3y2+2x2)
6 x superscript 3 baseline y superscript 2 baseline left parenthesis 3 y superscript 2 baseline plus 2 x superscript 2 baseline right parenthesis

3x3y2(6y2+4x2)
3 x superscript 3 baseline y superscript 2 baseline left parenthesis 6 y superscript 2 baseline plus 4 x superscript 2 baseline right parenthesis

6x5y4(3y2+2x2)
6 x superscript 5 baseline y superscript 4 baseline left parenthesis 3 y superscript 2 baseline plus 2 x superscript 2 baseline right parenthesis

6x3y2(3xy2+2x2y)
6 x superscript 3 baseline y superscript 2 baseline left parenthesis 3 x y superscript 2 baseline plus 2 x superscript 2 baseline y right parenthesis

Answer 1

To factor the expression \( 18x^3y^4 + 12x^5y^2 \), we need to find the greatest common factor (GCF) of the coefficients and the variable terms.

1. Coefficients: The GCF of 18 and 12 is 6.
2. Variable Terms:
   • For \(x\), the smallest exponent is 3 (from \(x^3\)).
   • For \(y\), the smallest exponent is 2 (from \(y^2\)).

Thus, the GCF of the entire expression is \(6x^3y^2\).

Now we can factor this out:

\[ 18x^3y^4 + 12x^5y^2 = 6x^3y^2(3y^2 + 2x^2) \]

Therefore, the correct response is:

6x³y²(3y² + 2x²)