Question 190655


{{{121x^2-100y^2}}} Start with the given expression.



{{{(11x)^2-100y^2}}} Rewrite {{{121x^2}}} as {{{(11x)^2}}}.



{{{(11x)^2-(10y)^2}}} Rewrite {{{100y^2}}} as {{{(10y)^2}}}.



Notice how we have a difference of squares {{{A^2-B^2}}} where in this case {{{A=11x}}} and {{{B=10y}}}.



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.



{{{(11x)^2-(10y)^2=(11x+10y)(11x-10y)}}} Plug in {{{A=11x}}} and {{{B=10y}}}.



So this shows us that {{{121x^2-100y^2}}} factors to {{{(11x+10y)(11x-10y)}}}.



In other words {{{121x^2-100y^2=(11x+10y)(11x-10y)}}}.