( 2 + 1)^6 - ( 2 - 1)^6 = - Vidyadip

MCQ

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

A
$101$
B
$70\sqrt 2 $
✓
$140\sqrt 2 $
D
$120\sqrt 2 $

✓

Answer

Correct option: C.

$140\sqrt 2 $

c
(c) ${(x + a)^n} - {(x - a)^n}$

$ = 2\,{[^n}{C_1}{x^{n - 1}}a + {\,^n}{C_3}{x^{n - 3}}{a^3} + {\,^n}{C_5}{x^{n - 5}}{a^5} + ......]$

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

$ = 2\,{[^6}{C_1}{(\sqrt 2 )^5}{(1)^1} + {\,^6}{C_3}{(\sqrt 2 )^3}{(1)^3} + {\,^6}{C_5}{(\sqrt 2 )^1}{(1)^5}]$

$\,\,\,{(\sqrt 2 + 1)^6} - {(\sqrt 2 - 1)^6} = 2[6 \times 4\sqrt 2 + 20 \times 2\sqrt 2 + 6\sqrt 2 ]$

$=2[24\sqrt 2 + 40\sqrt 2 + 6\sqrt 2 ] = 140\sqrt 2 $.

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