Squares Inside

A special pattern can be hidden behind a common factor. As written, $2x^{2}-50$ is not a difference of squares, because neither 2 nor 50 is a square number. Factor out the 2 to get $2\left(x^{2}-25\right)$. Now the difference of squares is inside the parentheses, and the answer is $2\left(x+5\right)\left(x-5\right)$.

Factoring out the greatest common factor can reveal a difference of squares or a perfect square trinomial. After you take out the GCF, check the expression inside for these patterns before you look for factor pairs.

Check for a pattern again after every step. If a parenthesis holds $x^{2}$ minus a square number, it is a difference of squares and it factors further. If a trinomial inside passes the perfect square test, it factors further too. The expression is factored completely only when no factor that is left can be factored again.