Question 88224
{{{y^2-81}}} Start with the given expression


Let {{{A^2=y^2}}} and {{{B^2=81}}}. So we get this:


{{{y^2-81=A^2-B^2}}}


Since {{{A^2=y^2}}}, A can be solved for:

{{{sqrt(A^2)=sqrt(y^2)}}} Take the square root of both sides


{{{A=y}}}


Since {{{B^2=81}}}, B can be solved for:

{{{sqrt(B^2)=sqrt(81)}}} Take the square root of both sides


{{{B=9}}}


Since we have a difference of squares, we can factor it like this:


{{{A^2-B^2=(A+B)(A-B)}}}




Now replace A and B

{{{y^2-81=(y+9)(y-9)}}} Plug in {{{A=y}}} and {{{B=9}}}


So the expression


{{{y^2-81}}}


factors to


{{{(y+9)(y-9)}}}


Notice that if you foil the factored expression, you get the original expression. This verifies our answer.