Maths: a^3 minus b^3?

Question

also

(a-b)^3 = ?

Answer 1

1)

x^3 - y^3 = (x - y)(x^2 + xy + y^2) (<== formula)

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

2)

(a - b)^3

= (a - b)(a - b)(a - b)

= (a*a - b*a - ab + b*b)(a - b)

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

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

= a^2*a - 2ab*a + b^2 * a - a^2*b + 2ab*b - b^2*b

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

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

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

Answer 2

I think that would be factorisation for the first?

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