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Math Help - Quadratic formula 4(a+b)√(16(a+2ab+b)-48ab) / 24

  1. #1
    Junior Member
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    Quadratic formula 4(a+b)√(16(a+2ab+b)-48ab) / 24

    Hi,

    I have a question in regard to a quadratic formula I'm solving.

    4(a+b)√(16(a+2ab+b)-48ab) / 24

    4(a+b)4√(a-ab+b) / 24

    I don't understand how +2ab became -ab and why -48ab disappeared.

    Anyone able to clarify that for me?

    Thanks
    David
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  2. #2
    MHF Contributor
    Grandad's Avatar
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    South Coast of England
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    Hello Splint

    Welcome to Math Help Forum!
    Quote Originally Posted by Splint View Post
    Hi,

    I have a question in regard to a quadratic formula I'm solving.

    4(a+b)√(16(a+2ab+b)-48ab) / 24

    4(a+b)4√(a-ab+b) / 24

    I don't understand how +2ab became -ab and why -48ab disappeared.

    Anyone able to clarify that for me?

    Thanks
    David
    Just remove the inner brackets inside the square root and simplify:

    \sqrt{\Big(16(a^2+2ab+b^2)-48ab\Big)}

    =\sqrt{(16a^2+32ab+16b^2-48ab)}

    =\sqrt{16a^2 -16ab+16b^2}

    =\sqrt{16}\sqrt{a^2-ab+b^2}

    =4\sqrt{a^2-ab+b^2}

    Grandad
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