Wyprowadź wzór na:
(a-b)¹¹ =
=(a-b)(a-b)²(a-b)²(a-b)²(a-b)²(a-b)²=
=(a-b)(a²-2ab+b²)(a²-2ab+b²)(a²-2ab+b²)(a²-2ab+b²)(a²-2ab+b²) =
=(a-b)(a⁴-2a³b+a²b²-2a³b+4a²b²-2ab³+a²b²-2ab³+b⁴)(a⁴-2a³b+a²b²-2a³b+4a²b²-2ab³+a²b²-2ab³+b⁴)(a²-2ab+b²) =
=(a-b)(a²-2ab+b²)(a⁴-4a³b+6a²b²-4ab³+b⁴)(a⁴-4a³b+6a²b²-4ab³+b⁴) =
=(a³-2a²b+ab²-a²b+2ab²-b³)
(a⁸-4a⁷b+6a⁶b²-4a⁵b³+a⁴b⁴-4a⁷b+16a⁶b²-24a⁵b³+16a⁴b⁴-4a³b⁵ +
+6a⁶b²-24a⁵b³+36a⁴b⁴-24a³b⁵+6a²b⁶ -4a⁵b³+16a⁴b⁴-24a³b⁵+16a²b⁶+
+a⁴b⁴-4a³b⁵+6a²b⁶-4ab⁷+b⁸)=
=(a³-3a²b+3ab²-b³)( a⁸-8a⁷b+28a⁶b²-56a⁵b³+70a⁴b⁴-56a³b⁵+28a²b⁶-4ab⁷+b⁸)=
=dalej nie mam sily liczyc, wlasnie doczytalam ze ma byc z pascala
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(a-b)¹¹ =
=(a-b)(a-b)²(a-b)²(a-b)²(a-b)²(a-b)²=
=(a-b)(a²-2ab+b²)(a²-2ab+b²)(a²-2ab+b²)(a²-2ab+b²)(a²-2ab+b²) =
=(a-b)(a⁴-2a³b+a²b²-2a³b+4a²b²-2ab³+a²b²-2ab³+b⁴)(a⁴-2a³b+a²b²-2a³b+4a²b²-2ab³+a²b²-2ab³+b⁴)(a²-2ab+b²) =
=(a-b)(a²-2ab+b²)(a⁴-4a³b+6a²b²-4ab³+b⁴)(a⁴-4a³b+6a²b²-4ab³+b⁴) =
=(a³-2a²b+ab²-a²b+2ab²-b³)
(a⁸-4a⁷b+6a⁶b²-4a⁵b³+a⁴b⁴-4a⁷b+16a⁶b²-24a⁵b³+16a⁴b⁴-4a³b⁵ +
+6a⁶b²-24a⁵b³+36a⁴b⁴-24a³b⁵+6a²b⁶ -4a⁵b³+16a⁴b⁴-24a³b⁵+16a²b⁶+
+a⁴b⁴-4a³b⁵+6a²b⁶-4ab⁷+b⁸)=
=(a³-3a²b+3ab²-b³)( a⁸-8a⁷b+28a⁶b²-56a⁵b³+70a⁴b⁴-56a³b⁵+28a²b⁶-4ab⁷+b⁸)=
=dalej nie mam sily liczyc, wlasnie doczytalam ze ma byc z pascala