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Math Help - [SOLVED] Sums and Differences of 2 Cubes

  1. #1
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    [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
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  2. #2
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    I'll use x instead of b to avoid confusion with the variables: x^3 - 8 = {\color{red}x}^3 - {\color{blue}2}^3

    ...........So our identity says: \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: \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)
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  3. #3
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    Quote Originally Posted by Needhelpatmaths View Post
    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 a^3-b^3=?? or b^3-2^3=??
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  4. #4
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    ok I think I got it

    Kk thankyou
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