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(x^2 - 25). Now the difference of squares is inside the parentheses, and the answer is 2(x + 5)(x - 5).

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.