Question 179427


{{{4s^2-100t^2}}} Start with the given expression



{{{4(s^2-25t^2)}}} Factor out the GCF {{{4}}}



Now let's focus on the inner expression {{{s^2-25t^2}}}



------------------------------------------------------------



{{{s^2-25t^2}}} Start with the inner expression.



{{{(s)^2-25t^2}}} Rewrite {{{s^2}}} as {{{(s)^2}}}.



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



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



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.



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



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



In other words {{{s^2-25t^2=(s+5t)(s-5t)}}}.

------------------------------------------------------------


So this means that {{{4(s^2-25t^2)}}} factors down further to {{{4(s+5t)(s-5t)}}}




=============================================

Answer:


So {{{4s^2-100t^2}}} completely factors to {{{4(s+5t)(s-5t)}}}