Question 385283
{{{p^2 - q^2 + r^2 - 2pr}}} Start with the given expression.



{{{p^2 - 2pr + r^2 - q^2  }}} Rearrange the terms.



{{{(p-r)^2 - q^2  }}} Factor {{{p^2 - 2pr + r^2}}} to get {{{(p-r)^2}}}



{{{(p-r+q)(p-r-q)  }}} Now use the difference of squares formula to factor.



So {{{p^2 - q^2 + r^2 - 2pr}}} factors to {{{(p-r+q)(p-r-q)  }}}



In other words, {{{p^2 - q^2 + r^2 - 2pr=(p-r+q)(p-r-q)  }}}