Question 183246
I'm assuming that you want to factor this.





{{{25v^2-9}}} Start with the given expression.



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



{{{(5v)^2-(3)^2}}} Rewrite {{{9}}} as {{{(3)^2}}}.



Notice how we have a difference of squares {{{A^2-B^2}}} where in this case {{{A=5v}}} and {{{B=3}}}.



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.



{{{(5v)^2-(3)^2=(5v+3)(5v-3)}}} Plug in {{{A=5v}}} and {{{B=3}}}.



So this shows us that {{{25v^2-9}}} factors to {{{(5v+3)(5v-3)}}}.



In other words {{{25v^2-9=(5v+3)(5v-3)}}}.