Chapter 8.5, Problem 19PPS

To determine

To factor: The polynomial $4a^2{b}^2+2a^{2}b-10a{b}^2$ using the Distributive Property

Answer to Problem 19PPS

  $2ab\left(2ab+a-5b\right)$

Explanation of Solution

Given:

  $4a^2{b}^2+2a^{2}b-10a{b}^2$

Calculation:

The Distributive Property is given by

  $a\left(b+c\right)=ab+ac\text{ and }ab+ac=a\left(b+c\right)$ , where a , b and c are real numbers

Now, in the given polynomial the GCF is $2ab$

So, factored out the GCF and use the distributive property

  $\begin{array}{l}4a^2{b}^2+2a^{2}b-10a{b}^2\\ =2ab\left(2ab+a-5b\right)\end{array}$

So, the factored form is $2ab\left(2ab+a-5b\right)$