Question 119393

{{{40-5t^3}}} Start with the given expression



{{{5(8-t^3)}}} Factor out the GCF {{{5}}}



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




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



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



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



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



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




{{{5(2-t)(4+2t+t^2)}}} Now reintroduce the GCF 





So {{{40-5t^3}}} factors to {{{5(2-t)(4+2t+t^2)}}}