Chapter 8.6, Problem 33PPS

To determine

To factor: The polynomial $x^2-6xy+5y^2$

Answer to Problem 33PPS

  $\left(x-5y\right)\left(x-y\right)$

Explanation of Solution

Given:

  $x^2-6xy+5y^2$

Calculation:

The given polynomial is $x^2-6xy+5y^2$

Rewrite the middle term as $-6xy=-5xy-xy$ . So, the polynomial becomes

  $x^2-5xy-xy+5y^2$

Make group as shown below

  $\left(x^2-5xy\right)+\left(-xy+5y^2\right)$

Factor out the GCF from each of the group

  $x\left(x-5y\right)-y\left(x-5y\right)$

Finally, factored out the common factor

  $\left(x-5y\right)\left(x-y\right)$

Therefore, the factored form of the given polynomial is $\left(x-5y\right)\left(x-y\right)$