Question

Factor Linear Expressions Quick Check
5 of 55 of 5 Items
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

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

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 in the two terms.

1. **Coefficients**: The coefficients are 18 and 12. The GCF of 18 and 12 is 6.

2. **Variables**: For the variable \( x \):
- The powers are \( x^3 \) and \( x^5 \). The GCF is \( x^3 \).

For the variable \( y \):
- The powers are \( y^4 \) and \( y^2 \). The GCF is \( y^2 \).

Combining these, the GCF of the entire expression \( 18x^3y^4 + 12x^5y^2 \) is \( 6x^3y^2 \).

Next, we factor \( 6x^3y^2 \) out of each term:

\[
6x^3y^2 \left( \frac{18x^3y^4}{6x^3y^2} + \frac{12x^5y^2}{6x^3y^2} \right)
\]

Simplifying the terms inside the parentheses:
- First term:
\[
\frac{18x^3y^4}{6x^3y^2} = 3y^2
\]
- Second term:
\[
\frac{12x^5y^2}{6x^3y^2} = 2x^2
\]

Putting it together, we have:
\[
6x^3y^2(3y^2 + 2x^2)
\]

Therefore, the expression can be rewritten as:

**Response**: \( 6x^3y^2(3y^2 + 2x^2) \)