Difference of the roots of quadratic formula

Question

I have a question to solve with roots quadratic formula that is ,

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

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

but I didn't understand how the below formula is generated;

$$\alpha^3 - \beta^3 = (\alpha-\beta)^3+3\alpha\beta(\alpha-\beta)$$

Answer 1

$(\alpha - \beta)^3 +3\alpha\beta(\alpha - \beta) = \alpha^3 -3\alpha^2\beta + 3\alpha\beta^2 -\beta^3+3\alpha^2\beta - 3\alpha\beta^2 =\alpha^3-\beta^3$

Answer 2

do you recognize that $(\alpha - \beta)$ is a factor of $\alpha^3 - \beta^3?$

can you do divide $\alpha^3 - \beta^3$ by $\alpha - \beta?$

simplify the quotient into the required from.