# How do you factor r^2-25tw+5wr-5tr?

May 14, 2015

It helps to swap the terms around a little first so that the coefficients of the 1st and 2nd terms are in the same ratio as the 3rd and 4th terms thus:

${r}^{2} - 25 t w + 5 w r - 5 t r$

$= {r}^{2} + 5 w r - 5 t r - 25 t w$

$= \left({r}^{2} + 5 w r\right) - \left(5 t r + 25 t w\right)$

$= r \left(r + 5 w\right) - 5 t \left(r + 5 w\right)$

$= \left(r - 5 t\right) \left(r + 5 w\right)$