Question 190756


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



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



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



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



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.



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



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



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