Chapter 8.6, Problem 34PPS

To determine

To factor: The polynomial $a^2+10ab-39b^2$

Answer to Problem 34PPS

  $\left(a+13b\right)\left(a-3b\right)$

Explanation of Solution

Given:

  $a^2+10ab-39b^2$

Calculation:

The given polynomial is $a^2+10ab-39b^2$

Rewrite the middle term as $10ab=13ab-3ab$ . So, the polynomial becomes

  $a^2+13ab-3ab-39b^2$

Make group as shown below

  $\left(a^2+13ab\right)+\left(-3ab-39b^2\right)$

Factor out the GCF from each of the group

  $a\left(a+13b\right)-3b\left(a+13b\right)$

Finally, factored out the common factor

  $\left(a+13b\right)\left(a-3b\right)$

Therefore, the factored form of the given polynomial is $\left(a+13b\right)\left(a-3b\right)$