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Math Help - algebra

  1. #1
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    algebra

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    (a-b)^2(a+b)+ab(a+b)=a^3+b^3
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  2. #2
    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by Crystal09 View Post
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    (a-b)^2(a+b)+ab(a+b)=a^3+b^3
    start with the left side. expand everything and cancel what should be canceled. then show you can get the left side. hopefully you didn't make a mistake with the signs, i haven't checked it yet
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  3. #3
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    Hello, Crystal09!

    Show that: . (a-b)^2(a+b)+ab(a+b)\:=\:a^3+b^3
    What's stopping you from multiply it out?


    If you looking for a deliberately complicated proof . . .


    We have: . a^3 + b^3

    Factor: . (a + b)(a^2-ab+b^2)

    Subtract and add ab\!:\;\;(a + b)(a^2 \:{\color{red}-\: ab}\: - ab + b^2 \:{\color{red}+\: ab}\,)

    And we have: . (a + b)(a^2 - 2ab + b^2 + ab)

    Factor: . (a+b)\left([a-b]^2 + ab\right)

    Distribute: . (a+b)(a-b)^2 +(a+b)ab \;=\;(a-b)^2(a+b) + ab(a+b)

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  4. #4
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    Yeah, what's stopping you from multiply it out?

    I can try to solve the half of the algebraic expression you're struggling with, in order to help you solving the remaining under;

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