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Math Help - Expanding Binomials using the Binomial Thm? (+radicals)

  1. #1
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    Expanding Binomials using the Binomial Thm? (+radicals)

    I am just having trouble with simplifying radicals within the binomial in conjunction w/ the bionomial thm. I understand how it works thus far and all of that...but these two problems (and the radicals) are messing me up.

    1. (a-2sqrt(3))^6
    2. (a-sqrt(2))^5
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  2. #2
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    Hello, puzzledwithpolynomials!

    It helps if you write out the terms completely ... then simplify.


    2)\;\;\left(a-\sqrt{2}\right)^5

    {5\choose5}(a^5)\left(\text{-}\sqrt{2}\right)^0 + {5\choose4}(a^4)\left(\text{-}\sqrt{2}\right)^1 + {5\choose3}(a^3)\left(\text{-}\sqrt{2}\right)^2 + {5\choose2}(a^2)\left(\text{-}\sqrt{2}\right)^3 + {5\choose1}(a^1)\left(\text{-}\sqrt{2}\right)^4 + {5\choose0}(a^0)\left(\text{-}\sqrt{2}\right)^5

    . . = \;\;1\cdot a^6\cdot1 \;+\; 5(a^4)\left(\text{-}\sqrt{2}\right) \;+ \;10(a^3)(2) \;+ \;10(a^2)\left(\text{-}2\sqrt{2}\right) \;+\; 5(a)(4) \;+ \;1(1)\left(\text{-}4\sqrt{2}\right)

    . . = \;\;a^5 - 5\sqrt{2}\,a^4 + 20a^3 - 20\sqrt{2}\,a^2 + 20a - 4\sqrt{2}

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  3. #3
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    Thank you! I see how I should deal with these radicals.
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