Question 179426


{{{25y^2-49w^2}}} Start with the given expression.



{{{(5y)^2-49w^2}}} Rewrite {{{25y^2}}} as {{{(5y)^2}}}.



{{{(5y)^2-(7w)^2}}} Rewrite {{{49w^2}}} as {{{(7w)^2}}}.



Notice how we have a difference of squares {{{A^2-B^2}}} where in this case {{{A=5y}}} and {{{B=7w}}}.



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.



{{{(5y)^2-(7w)^2=(5y+7w)(5y-7w)}}} Plug in {{{A=5y}}} and {{{B=7w}}}.



So this shows us that {{{25y^2-49w^2}}} factors to {{{(5y+7w)(5y-7w)}}}.



In other words {{{25y^2-49w^2=(5y+7w)(5y-7w)}}}.