How do you factor completely 24r^2s^2 - 9t^2u^2?

Aug 2, 2016

$3 \left(8 {r}^{2} {s}^{2} - 3 {t}^{2} {u}^{2}\right)$

Explanation:

Always look for a common factor first.

$24 {r}^{2} {s}^{2} - 9 {t}^{2} {u}^{2}$

=$3 \left(8 {r}^{2} {s}^{2} - 3 {t}^{2} {u}^{2}\right)$

This does not factor further.

However, if the expression had been:

$25 {r}^{2} {s}^{2} - 9 {t}^{2} {u}^{2}$ we would have had difference of squares.

=$\left(5 r s + 3 t u\right) \left(5 r s - 3 t u\right)$