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: \[ \boxed{6x^3y^2(3y^2 + 2x^2)} \]