Question

use the distributive property to factor the polynomial. $4a^{2}b^{2}+2a^{2}b-10ab^{2}$ (select choice )( select choice )

Explanation:

Step1: Identify greatest common factor

Find GCF of coefficients and variables:

• Coefficients: GCF of 4, 2, 10 is 2
• Variables: GCF of $a^2b^2$, $a^2b$, $ab^2$ is $ab$

Overall GCF: $2ab$

Step2: Factor out GCF via distribution

Divide each term by $2ab$:
$\frac{4a^2b^2}{2ab} + \frac{2a^2b}{2ab} - \frac{10ab^2}{2ab} = 2ab + a - 5b$
Rewrite polynomial as product of GCF and remaining terms.

Answer:

$2ab$ $(2ab + a - 5b)$