Need help with algebraic fraction problem.

[chocoholic8a]

I was wondering if you could help me with a algebraic fraction problem. I do online school, and I'm having difficulty understanding my teachers explanation. Basically he gives partial answers and I need it broken down and explained to me. This is one of the problems...
a^4/ 2a^2-4a^4 times 8a^3+1/ 2a+4a^2

Thank you very much for your time and consideration!!

 

[galactus]

Please use proper grouping symbols. I assume this is what you mean?:

\(\displaystyle \frac{a^{4}}{2a^{2}-4a^{4}}\cdot\frac{8a^{3}+1}{2a+4a^{2}}\)

Notice that \(\displaystyle 8a^{3}+1=(2a)^{3}+(1)^{3}\) is the sum of two cubes.

\(\displaystyle \frac{a^{4}}{2a^{2}(1-2a^{2})}\cdot \frac{(2a)^{3}+1}{2a(1+2a)}\)

Now, factor the sum of two cubes, do some cancellations and simplify.

 

[Aladdin]

A3 + B3 = (A + B)(A2 - AB + B2)

 

[Denis]

A3 + B3 = (A + B)(A2 - AB + B2)

A^3 + B^3 = (A + B)(A^2 - AB + B^2)

 

[chocoholic8a]

what im having a hard time with is factoring...can u explain to me how to factor equations?

 

[Denis]

...can u explain to me how to factor equations?

No. Use Google; you'll get sites like: http://math.usask.ca/emr/factor.html