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

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- Feb 10th 2009, 09:20 PMNeedhelpatmaths[SOLVED] Sums and Differences of 2 Cubes
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 - Feb 10th 2009, 09:38 PMo_O
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: $\displaystyle \overbrace{{\color{red}x}^3 - {\color{blue}2}^3} = ({\color{red}x} - {\color{blue}2})({\color{red}x}^2 + {\color{blue}2}{\color{red}x} + {\color{blue}2}^2) = (x-2)(x^2 + 2x + 4)$ - Feb 10th 2009, 09:41 PMmathaddict
- Feb 10th 2009, 09:43 PMNeedhelpatmathsok I think I got it
Kk thankyou