Question 190662


{{{x^2-49}}} Start with the given expression.



{{{(x)^2-49}}} Rewrite {{{x^2}}} as {{{(x)^2}}}.



{{{(x)^2-(7)^2}}} Rewrite {{{49}}} as {{{(7)^2}}}.



Notice how we have a difference of squares {{{A^2-B^2}}} where in this case {{{A=x}}} and {{{B=7}}}.



So let's use the difference of squares formula {{{A^2-B^2=(A+B)(A-B)}}} to factor the expression:



{{{A^2-B^2=(A+B)(A-B)}}} Start with the difference of squares formula.



{{{(x)^2-(7)^2=(x+7)(x-7)}}} Plug in {{{A=x}}} and {{{B=7}}}.



So this shows us that {{{x^2-49}}} factors to {{{(x+7)(x-7)}}}.



In other words {{{x^2-49=(x+7)(x-7)}}}.