Question 190755


{{{16x^2-4y^2}}} Start with the given expression.



{{{(4x)^2-4y^2}}} Rewrite {{{16x^2}}} as {{{(4x)^2}}}.



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



Notice how we have a difference of squares {{{A^2-B^2}}} where in this case {{{A=4x}}} and {{{B=2y}}}.



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.



{{{(4x)^2-(2y)^2=(4x+2y)(4x-2y)}}} Plug in {{{A=4x}}} and {{{B=2y}}}.



So this shows us that {{{16x^2-4y^2}}} factors to {{{(4x+2y)(4x-2y)}}}.



In other words {{{16x^2-4y^2=(4x+2y)(4x-2y)}}}.