Question 1126153
{{{ (v-2u)^2-(2u-v)(u+2v)-2v+4u }}}
= {{{ (v-2u)^2 + ((v-2u)(u+2v)) + (-2)(v-2u) }}}<br>

Factoring out the common {{{ (v-2u) }}} :
= {{{ (v-2u)  ( (v-2u) + (u+2v) -2  )  }}}
= {{{ highlight ( (v-2u) ( 3v-u-2 ))  }}}

which is equivalent to {{{  highlight ( (2u-v) ( u-3v+2 ))  }}} <br>

I encourage you to multiply this result out, and the original expression as well.  Then compare them to prove to yourself that they are indeed equal.