How do you factor $r^{2} - 25 t w + 5 w r - 5 t r$ $r^2-25tw+5wr-5tr$ ?

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How do you factor $r^{2} - 25 t w + 5 w r - 5 t r$ $r^2-25tw+5wr-5tr$ ?

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Answer 1 · 2015-05-14T21:30:24

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:

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

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

$= (r^{2} + 5 w r) - (5 t r + 25 t w)$ $= (r^2+5wr)-(5tr+25tw)$

$= r (r + 5 w) - 5 t (r + 5 w)$ $= r(r+5w)-5t(r+5w)$

$= (r - 5 t) (r + 5 w)$ $= (r-5t)(r+5w)$

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How do you factor $r^{2} - 25 t w + 5 w r - 5 t r$ $r^2-25tw+5wr-5tr$ ?

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