Algebra Question

[wooden zealot]

I know that the difference of squares says that a^2-b^2=(a+b)(a-b), and the difference of cubes says that (a-b)(a^2+ab+b^2)=a^3-b^3 and so on. But how exactly are these formulas derived? Im wondering if theres a way to show a proof without having a visual representation, i.e an algebra way of proving it