How do you do these?
This is the formula and a sample question.
a^3 + b^3 = (a + b)(a^2 - ab + b^2)
b^3 - 8
Please, someone elxplain this to me
* ^ means power
I'll use $\displaystyle x$ instead of $\displaystyle b$ to avoid confusion with the variables: $\displaystyle x^3 - 8 = {\color{red}x}^3 - {\color{blue}2}^3$
...........So our identity says: $\displaystyle \underbrace{{\color{red}a}^3 - {\color{blue}b}^3}_{\displaystyle \downarrow} = ({\color{red}a} - {\color{blue}b})({\color{red}a}^2 + {\color{red}a}{\color{blue}b} + {\color{blue}b}^2)$
So directly sub in our values: $\displaystyle \overbrace{{\color{red}x}^3 - {\color{blue}2}^3} = ({\color{red}x} - {\color{blue}2})({\color{red}x}^2 + {\color{blue}2}{\color{red}x} + {\color{blue}2}^2) = (x-2)(x^2 + 2x + 4)$