Question

How would you rewrite the expression 18x3y4+12x5y2 by factoring out the GCF?(1 point) Responses 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) 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(3y2+2x2)

Answer 1

To factor out the GCF (Greatest Common Factor) from the expression \(18x^3y^4 + 12x^5y^2\), we first determine the GCF of the coefficients and the variables separately.

1. **Coefficients**: The coefficients are 18 and 12. The GCF of 18 and 12 is 6.
2. **Variable Terms**:
- For \(x\): The minimum exponent in \(x^3\) and \(x^5\) is \(x^3\).
- For \(y\): The minimum exponent in \(y^4\) and \(y^2\) is \(y^2\).

Now we can combine these to get the GCF for the entire expression:
\[
\text{GCF} = 6x^3y^2
\]

Next, we divide each term in the original expression by the GCF:
- For \(18x^3y^4\):
\[
\frac{18x^3y^4}{6x^3y^2} = 3y^2
\]

- For \(12x^5y^2\):
\[
\frac{12x^5y^2}{6x^3y^2} = 2x^2
\]

Now we can rewrite the expression by factoring out the GCF:
\[
18x^3y^4 + 12x^5y^2 = 6x^3y^2(3y^2 + 2x^2)
\]

Thus, the rewritten expression is:
\[
\boxed{6x^3y^2(3y^2 + 2x^2)}
\]