Chapter 8.5, Problem 3CYU

To determine

To factor: The polynomial $10g^2{h}^2+9g{h}^2-g^{2}h$ using the distributive property

Answer to Problem 3CYU

  $gh\left(10gh+9h-g\right)$

Explanation of Solution

Given:

  $10g^2{h}^2+9g{h}^2-g^{2}h$

Calculation:

The given polynomial is $10g^2{h}^2+9g{h}^2-g^{2}h$

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 $gh$

So, factored out the GCF and use the distributive property

  $\begin{array}{l}10g^2{h}^2+9g{h}^2-g^{2}h\\ =gh\left(10gh+9h-g\right)\end{array}$

So, the factored form is $gh\left(10gh+9h-g\right)$