Question 190652

{{{25x^2-1}}} Start with the given expression.



{{{(5x)^2-1}}} Rewrite {{{25x^2}}} as {{{(5x)^2}}}.



{{{(5x)^2-(1)^2}}} Rewrite {{{1}}} as {{{(1)^2}}}.



Notice how we have a difference of squares {{{A^2-B^2}}} where in this case {{{A=5x}}} and {{{B=1}}}.



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.



{{{(5x)^2-(1)^2=(5x+1)(5x-1)}}} Plug in {{{A=5x}}} and {{{B=1}}}.



So this shows us that {{{25x^2-1}}} factors to {{{(5x+1)(5x-1)}}}.



In other words {{{25x^2-1=(5x+1)(5x-1)}}}.