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Math Help - factorising

  1. #1
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    factorising

    i've now got the question: factorise: x^3 - a^3 but i don't know what to do when its only letters involved without the help of any numbers, could someone show me how to do it this way?

    thanks
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  2. #2
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    e^(i*pi)'s Avatar
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    Quote Originally Posted by mark View Post
    i've now got the question: factorise: x^3 - a^3 but i don't know what to do when its only letters involved without the help of any numbers, could someone show me how to do it this way?

    thanks
    This is a standard factorisation known as the difference of two cubes. Normally a and b are used but I picked p and q since a is used in the question.

    p^3 - q^3 = (p - q)(p^2 + pq + q^2)

    In your example p = x and q = a
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  3. #3
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    i tried that formula out but it didn't seem to work. say i put p = 4 and q = 2 the equation would be 4^3 - 2^3 = 64 - 8 = 56 so then it would be (4 - 2)(4^2 + 4(-2) + -2^2) which then leads to 2(16 - 8 + 4) then 32 - 16 + 8 = 24 ,so obviously not 56. whats gone wrong here?
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  4. #4
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    Quote Originally Posted by mark View Post
    i tried that formula out but it didn't seem to work. say i put p = 4 and q = 2 the equation would be 4^3 - 2^3 = 64 - 8 = 56 so then it would be (4 - 2)(4^2 + 4(-2) + -2^2) which then leads to 2(16 - 8 + 4) then 32 - 16 + 8 = 24 ,so obviously not 56. whats gone wrong here?
    You treated q as -q. The sign is already taken into account and it's treated as positive

    4^3 - 2^3 = (4-2)(4^2+4(2)+(2)^2) = 2(16+8+4) = 56
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  5. #5
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    ah i see thanks, silly mistake there
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