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Math Help - Algebraic question

  1. #1
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    Algebraic question

    If a, b, c are positive numbers, deduce that (a+ + b)(b+ c)(c + a) ≥ 8abc.
    Can someone list the steps to do this q please?
    Thanks.
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  2. #2
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    Expand the left hand side out, what do you get?
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  3. #3
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    2abc + a^2 (b + c) + b^2 (a + c) c^2 (a + b)
    is that right? If so what do i do now?
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  4. #4
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    Quote Originally Posted by Detanon View Post
    2abc + a^2 (b + c) + b^2 (a + c) c^2 (a + b)
    is that right? If so what do i do now?
    You haven't completely expanded it yet: a^2(b+ c)= a^2b+ a^2c, etc.
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