Question 190658


{{{-81+x^2}}} Start with the given expression.



{{{x^2-81}}} Rearrange the terms.



{{{(x)^2-81}}} Rewrite {{{x^2}}} as {{{(x)^2}}}.



{{{(x)^2-(9)^2}}} Rewrite {{{81}}} as {{{(9)^2}}}.



Notice how we have a difference of squares {{{A^2-B^2}}} where in this case {{{A=x}}} and {{{B=9}}}.



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-(9)^2=(x+9)(x-9)}}} Plug in {{{A=x}}} and {{{B=9}}}.



So this shows us that {{{-81+x^2}}} factors to {{{(x+9)(x-9)}}}.



In other words {{{-81+x^2=(x+9)(x-9)}}}.