Question 481878


{{{81-25w^2}}} Start with the given expression.



{{{(9)^2-25w^2}}} Rewrite {{{81}}} as {{{(9)^2}}}.



{{{(9)^2-(5w)^2}}} Rewrite {{{25w^2}}} as {{{(5w)^2}}}.



Notice how we have a difference of squares {{{A^2-B^2}}} where in this case {{{A=9}}} and {{{B=5w}}}.



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.



{{{(9)^2-(5w)^2=(9+5w)(9-5w)}}} Plug in {{{A=9}}} and {{{B=5w}}}.



So this shows us that {{{81-25w^2}}} factors to {{{(9+5w)(9-5w)}}}.



In other words {{{81-25w^2=(9+5w)(9-5w)}}}.