Question 527942


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



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



{{{(5b)^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=5b}}} 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.



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



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



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



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