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Math Help - Algebra problem

  1. #1
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    Algebra problem

    I had an assignment recently where I had to derive the formula for the volume of a fulcrum. While simplifying i found that an expression (a^3-b^3)*(c/a-b) will evaluate to (a^2+ab+b^2) but I do not understand how, could someone please explain how this expands?
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  2. #2
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    I don't see how (a^3-b^3)*(c/a-b) can simplify to (a^2+ab+b^2). One reason is that the first expression contains c, but the second one does not. On the other hand, (a^3-b^3)*c/(a-b) simplifies to (a^2+ab+b^2)*c, which can be checked by multiplying (a^2+ab+b^2) and (a-b).
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  3. #3
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    Yeah I meant (a^2+ab+b^2)c and I have checked on my calculator but i would just like someone to explain how that works out
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  4. #4
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    Do you need explanation how to multiply (a^2+ab+b^2) and (a-b)? Use the distributivity law: multiply each term from the first factor by each term of the second factor and add all of the results together.
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  5. #5
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    I would like someone to explain how(a^3-b^3)*(c/a-b) evaluates to c*(a^2+ab+b^2)
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  6. #6
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    Quote Originally Posted by stripe501 View Post
    I would like someone to explain how(a^3-b^3)*(c/a-b) evaluates to c*(a^2+ab+b^2)
    You were already told that a^3 - b^3 = (a^2 + ab + b^2) * (a - b) ; so simply cancel out the (a - b) terms.
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  7. #7
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    Quote Originally Posted by stripe501 View Post
    I would like someone to explain how(a^3-b^3)*(c/a-b) evaluates to c*(a^2+ab+b^2)
    It does not, but (a^3-b^3)*c/(a-b) does.
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  8. #8
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    Quote Originally Posted by stripe501 View Post
    I would like someone to explain how(a^3-b^3)*(c/a-b) evaluates to c*(a^2+ab+b^2)
    You do it like the rest of us have had to. Multiply out (a - b)*(a^2 + ab + b^2) = a^3 - b^3 and note it for reference the next time you see it.

    So you get




    -Dan
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  9. #9
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    Algebra problem

    Hi stripe501,
    A fulcrum is a support or wedge about which a lever turns
    A frustum is part of a conical or pyramid object formed by cutting off apart of the top parallel to the base.Your equation does not appear to address either one of these shapes


    bjh
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