7. binomial theoram — ગણિત ધોરણ 11 સાયન્સ — Question

$ = 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 $.