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

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

3x3y2(6y2+4x2)

Answer 1

To factor the expression \( 18x^3y^4 + 12x^5y^2 \) by finding the greatest common factor (GCF), we first identify the GCF of the coefficients and the variables.

1. Coefficients: The GCF of 18 and 12 is 6.
2. Variable \( x \): The minimum power of \( x \) in both terms is \( x^3 \).
3. Variable \( y \): The minimum power of \( y \) in both terms is \( y^2 \).

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

Now we factor this out from each term:

\[ 18x^3y^4 = 6x^3y^2 \cdot 3y^2 \]

\[ 12x^5y^2 = 6x^3y^2 \cdot 2x^2 \]

Putting it all together gives:

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

Therefore, the correct rewrite of the expression by factoring out the GCF is:

6x³y²(3y² + 2x²).