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Math Help - Help with simplification

  1. #1
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    Help with simplification

    Can someone please help me and explain each step to simplify the following:

    2t^3-2(t+h)^3

    I know the answer is:

    -6t^2h-6th^2-2h^3

    But I want to know how to get that simplification. I don't quite understand how to. Thanks.
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  2. #2
    MHF Contributor harish21's Avatar
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    Quote Originally Posted by softwareguy View Post
    Can someone please help me and explain each step to simplify the following:

    2t^3-2(t+h)^3

    I know the answer is:

    -6t^2h-6th^2-2h^3

    But I want to know how to get that simplification. I don't quite understand how to. Thanks.
     (a+b)^3 = {a^3}+{b^3}+3{a^2}b+3a{b^2}

    so you have ,

    2{t^3} - 2 ({t^3}+{h^3}+3t{h^2}+3h{t^2})

    = 2{t^3} - 2{t^3}- 2{h^3}-6t{h^2}-6h{t^2}

    = -2{h^3}-6t{h^2}-6h{t^2}

    = -6t^2h-6th^2-2h^3
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  3. #3
    Super Member Anonymous1's Avatar
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    Note that,

    (a+b)^3 = (a+b)(a+b)(a+b)= (a^2 + 2ab + b^2)(a+b) = a^3 + 3a^2b + 3ab^2 + b^3
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  4. #4
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    Thank you so much guys!
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