Question 119396

{{{4t^5-32t^2}}} Start with the given expression



{{{4t^2(t^3-8)}}} Factor out the GCF {{{4t^2}}}



Now let's focus on the inner expression {{{t^3-8}}}



{{{t^3-8}}} Start with the inner expression.



{{{(t)^3-(2)^3}}} Rewrite {{{t^3}}} as {{{(t)^3}}}. Rewrite {{{8}}} as {{{(2)^3}}}.



{{{(t-2)((t)^2+(t)(2)+(2)^2)}}} Now factor by using the difference of cubes formula. Remember the <a href="http://www.purplemath.com/modules/specfact2.htm">difference of cubes formula</a> is {{{A^3-B^3=(A-B)(A^2+AB+B^2)}}}



{{{(t-2)(t^2+2t+4)}}} Multiply



So {{{t^3-8}}} factors to {{{(t-2)(t^2+2t+4)}}}.




{{{4t^2(t-2)(t^2+2t+4)}}} Now reintroduce the GCF {{{4t^2}}} 





So {{{4t^5-32t^2}}} factors to {{{4t^2(t-2)(t^2+2t+4)}}}