# How do you use the difference of two squares formula to factor 25x^6 - a44y^10?

May 14, 2015

I think the formula in the question should be $25 {x}^{6} - 144 {y}^{10}$.

On the assumption that I am correct, notice that:

$25 {x}^{6} - 144 {y}^{10} = {\left(5 {x}^{3}\right)}^{2} - {\left(12 {y}^{5}\right)}^{2}$

The right hand side is of the form ${a}^{2} - {b}^{2}$, so it factors as $\left(a + b\right) \left(a - b\right)$ as follows:

${\left(5 {x}^{3}\right)}^{2} - {\left(12 {y}^{5}\right)}^{2} = \left(5 {x}^{3} + 12 {y}^{5}\right) \left(5 {x}^{3} - 12 {y}^{5}\right)$