SOLUTION: Factor 4a^5-500a^2. I started by removing the greatest common factor. 4a^2(a^3-125) I am pretty sure that from this point it is a difference of cubes, but I am unsure as to how

Question 557686: Factor 4a^5-500a^2.
I started by removing the greatest common factor.
4a^2(a^3-125)
I am pretty sure that from this point it is a difference of cubes, but I am unsure as to how I am suppose to come up with the final answer. This is due today. Thank you!
Found 2 solutions by jim_thompson5910, nerdybill:
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
You are correct, is a difference of cubes since is a perfect cube and is also a perfect cube.

So becomes and we can use the difference of cubes formula to get

which simplifies to

So which means that completely factors to

In other words, for all values of 'a'.

If you need more help, email me at jim_thompson5910@hotmail.com

Also, please consider visiting my website: http://www.freewebs.com/jimthompson5910/home.html and making a donation. Thank you

Jim
Answer by nerdybill(7384) (Show Source): You can put this solution on YOUR website!
"difference of cubes":
a^3 � b^3 = (a � b)(a^2 + ab + b^2)
.
since you have:
4a^2(a^3-125)
we can rewrite as:
4a^2(a^3-5^3)
so, now we have:
4a^2(a-5)(a^2-5a+5^2)
4a^2(a-5)(a^2-5a+25)

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