Factorize a^3-b^3 (O Level Math Tuition Question)

(a-b)^3=a^3-3a^2b+3ab^2-b^3

So,
\begin{array}{rcl}  a^3-b^3&=&(a-b)^3+3a^2b-3ab^2\\  &=&(a-b)(a-b)^2+3a^2b-3ab^2\\  &=&(a-b)(a^2-2ab+b^2)+(a-b)(3ab)\\  &=&(a-b)(a^2+ab+b^2)  \end{array}

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5 Responses to Factorize a^3-b^3 (O Level Math Tuition Question)

  1. Paperpc@yahoo.com.sg says:

    How do we get (a-b)^3=a^3-3a^2b+3ab^2-b^3 if it is not (a-b)(a-b)(a-b)

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  2. Hi, yes, you are right, (a-b)^3 is (a-b)(a-b)(a-b).
    Continue to expand, you will get (a^2-2ab+b^2)(a-b)=a^3-2a^2b+ab^2-a^2b+2ab^2-b^3=a^3-3a^2b+3ab^2-b^3.
    Hope it helps!

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  3. tomcircle says:

    There is one challenging USA Math Olympiad 1997 (USA) question using this technique, see
    my blog at:
    http://tomcircle.wordpress.com/2013/05/07/imo-technique/

    Like

  4. Your blogs seems to me a great place for math lovers. I love to solve math problems…so this is the right place for me…Thanks for sharing o level maths here.

    Like

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