How do I factor this polynomial?

Question

anonymous · Answer

$$a ^{6}+b ^{3}$$

smarty · Answer

is that a^6?+b^2?

anonymous · Answer

b^3

vishweshshrimali5 · Answer

$$a^6 + b^3= (a^2+b)(a^4+b^2-a^2b)$$

I have used this formula

$$x^3+y^3 = (x+y)(x^2-xy+y^2)$$

anonymous · Answer

I don't get the formula..

anonymous · Answer

and how it fits the problem.

anonymous · Answer

do you remember the difference of squares factorization i gave earlier? it is only 1 of mostly three you need to "memorize"... look at page 2, the fatoring formulas here: http://tutorial.math.lamar.edu/pdf/Algebra_Cheat_Sheet.pdf

anonymous · Answer

the one he gave is called the sum of cubes fromula:  $\large a^3+b^3=(a+b)(a^2-2ab+b^2) $

vishweshshrimali5 · Answer

Right @dpaInc 
Very correct
and a nice cheat sheet

anonymous · Answer

notice you can write $\large a^6=(a^2)^3 $
so now you actually have a sum of cubes:  $\large (a^2)^3+b^3 $

anonymous · Answer

Yup, but there's more to that right?

anonymous · Answer

just use the formula now....

anonymous · Answer

i don't think there's more to it...

anonymous · Answer

:)

anonymous · Answer

why does the a become a a^4?

anonymous · Answer

because now your a is actually a^2... so when you plug it into the formula (a^2)^2 = a^4

anonymous · Answer

if i were to ask you to factor this:  $\large z^3+b^3 $
would you be able to?

anonymous · Answer

Why does the b become a b^2 when the formula says to multiply?

anonymous · Answer

ok... hang on....

anonymous · Answer

I'm not sure. I don't think I would be able to.

anonymous · Answer

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