[SOLVED] Sums and Differences of 2 Cubes

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• Feb 10th 2009, 09:20 PM
Needhelpatmaths
[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 PM
o_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 PM
mathaddict
Quote:

Originally Posted by Needhelpatmaths
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 guess you will have to be more specific in your question . I only see the formula . Perhaps you mean \$\displaystyle a^3-b^3=?? \$ or \$\displaystyle b^3-2^3=??\$
• Feb 10th 2009, 09:43 PM
Needhelpatmaths
ok I think I got it
Kk thankyou