Question 190656


{{{x^2y^2-4}}} Start with the given expression.



{{{(xy)^2-4}}} Rewrite {{{x^2y^2}}} as {{{(xy)^2}}}.



{{{(xy)^2-(2)^2}}} Rewrite {{{4}}} as {{{(2)^2}}}.



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



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.



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



So this shows us that {{{x^2y^2-4}}} factors to {{{(xy+2)(xy-2)}}}.



In other words {{{x^2y^2-4=(xy+2)(xy-2)}}}.