(sqrt{2} + 1)^6 - (sqrt{2} - 1)^6 = | vedclass

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(C) Using the binomial expansion formula: $(x + a)^n - (x - a)^n = 2[\binom{n}{1}x^{n-1}a + \binom{n}{3}x^{n-3}a^3 + \binom{n}{5}x^{n-5}a^5 + \dots]$F

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$140\sqrt{2}$

Vedclass · Answer

(C) Using the binomial expansion formula: $(x + a)^n - (x - a)^n = 2[\binom{n}{1}x^{n-1}a + \binom{n}{3}x^{n-3}a^3 + \binom{n}{5}x^{n-5}a^5 + \dots]$For $n=6, x=\sqrt{2}, a=1$:$(\sqrt{2} + 1)^6 - (\sqrt{2} - 1)^6 = 2[\binom{6}{1}(\sqrt{2})^5(1)^1 + \binom{6}{3}(\sqrt{2})^3(1)^3 + \binom{6}{5}(\sqrt{2})^1(1)^5]$$= 2[6 	imes 4\sqrt{2} + 20 	imes 2\sqrt{2} + 6 	imes \sqrt{2}]$$= 2[24\sqrt{2} + 40\sqrt{2} + 6\sqrt{2}]$$= 2[70\sqrt{2}] = 140\sqrt{2}$.

$(\sqrt{2} + 1)^6 - (\sqrt{2} - 1)^6 = $

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