Hi, usually the standard way to prove that a^3-b^3=(a-b)(a^2+ab+b^2)Chan09 wrote:Need some help:

Factorise a^3-b^3

Hint is (a-b)^3 and answer is (a-b)(a^2+ab+b^2)

I think:

(a-b)(a-b)(a-b) but then a^2-b^2= (a-b)(a+b)

is to expand (a-b)(a^2+ab+b^2)=a^3+a^2b+ab^2-a^2b-ab^2-b^3 and cancel out the terms.

Using hint is possible too,

(a-b)^3=a^3-3a^2b+3ab^2-b^3

So, a^3-b^3=(a-b)^3+3a^2b-3ab^2

=(a-b)(a-b)^2+3a^2b-3ab^2

=(a-b)(a^2-2ab+b^2)+(a-b)(3ab)

=(a-b)(a^2+ab+b^2)

Hope it helps!

I have also typed out the solution in LaTeX on my website:

http://mathtuition88.wordpress.com/2013 ... atex-a-b3/