Question

Explain how you can prove the difference of two cubes identity. a^3 – b^3 = (a – b)(a^2 + ab + b^2)

Answer 1

is this a mutiple choice or is this a  give an example type deal

Answer 2

I already calculated this

Let a^3 - b^3 = ?

Add on both th side -3a^2b + 3ab^2

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

-3a^2b+3ab^2

The firs equation is = (a - b)^3

Then,

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

Passing -3a^2b + 3ab^2 to the left side:
But changing the sinal

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

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

Putting (a - b) as commun factor

? = (a - b).[ 3ab + (a - b)^2 ]

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

Then,

? = (a - b).[ 3ab + a^2 -2ab +b^2]

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

I hope this has helped