SOLUTION: how do you factor 125t cubed+8. our book gives this answer: (5t + 2)(25t squared- 10t+ 4) thank you!

Algebra ->  Complex Numbers Imaginary Numbers Solvers and Lesson -> SOLUTION: how do you factor 125t cubed+8. our book gives this answer: (5t + 2)(25t squared- 10t+ 4) thank you!      Log On


   

Question 192338: how do you factor 125t cubed+8. our book gives this answer:
(5t + 2)(25t squared- 10t+ 4)
thank you!
Answer by nerdybill(7384) About Me  (Show Source):
You can put this solution on YOUR website!
125t^3 + 8
.
What you're suppose to see is that this is the same as:
(5t)^3 + 2^3
Which is a special case -- "sum of cubes".
See this web site for additional info:
http://www.purplemath.com/modules/specfact2.htm
.
a^3 + b^3 = (a + b)(a^2 – ab + b^2)
In your case:
a is 5t
b is 2
.
Therefore:
125t^3 + 8
= (5t)^3 + 2^3
= (5t + 2)((5t)^2 - (5t)(2) + 2^2)
= (5t + 2)(25t^2 - 10t + 4)