Question 618191


{{{4p^2-25}}} Start with the given expression.



{{{(2p)^2-25}}} Rewrite {{{4p^2}}} as {{{(2p)^2}}}.



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



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



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.



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



So this shows us that {{{4p^2-25}}} factors to {{{(2p+5)(2p-5)}}}.



In other words {{{4p^2-25=(2p+5)(2p-5)}}}.