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受欢迎的代数 >

展开 (2x+tan(7x))^9

解答

展开

(2 x + tan (7 x))^{9}

解答

512 x^{9} + 2304 x^{8} tan (7 x) + 4608 x^{7} tan^{2} (7 x) + 5376 x^{6} tan^{3} (7 x) + 4032 x^{5} tan^{4} (7 x) + 2016 x^{4} tan^{5} (7 x) + 672 x^{3} tan^{6} (7 x) + 144 x^{2} tan^{7} (7 x) + 18 x tan^{8} (7 x) + tan^{9} (7 x)

求解步骤

(2 x + tan (7 x))^{9}

使用二项式定理:

(a + b)^{n} = i = 0 \sum n (i n) a^{(n - i)} b^{i}

a = 2 x, b = tan (7 x)

= i = 0 \sum 9 (i 9) (2 x)^{(9 - i)} tan^{i} (7 x)

展开求和

= \frac{9 !}{0 ! ( 9 - 0 ) !} (2 x)^{9} tan^{0} (7 x) + \frac{9 !}{1 ! ( 9 - 1 ) !} (2 x)^{8} tan^{1} (7 x) + \frac{9 !}{2 ! ( 9 - 2 ) !} (2 x)^{7} tan^{2} (7 x) + \frac{9 !}{3 ! ( 9 - 3 ) !} (2 x)^{6} tan^{3} (7 x) + \frac{9 !}{4 ! ( 9 - 4 ) !} (2 x)^{5} tan^{4} (7 x) + \frac{9 !}{5 ! ( 9 - 5 ) !} (2 x)^{4} tan^{5} (7 x) + \frac{9 !}{6 ! ( 9 - 6 ) !} (2 x)^{3} tan^{6} (7 x) + \frac{9 !}{7 ! ( 9 - 7 ) !} (2 x)^{2} tan^{7} (7 x) + \frac{9 !}{8 ! ( 9 - 8 ) !} (2 x)^{1} tan^{8} (7 x) + \frac{9 !}{9 ! ( 9 - 9 ) !} (2 x)^{0} tan^{9} (7 x)

化简

\frac{9 !}{0 ! ( 9 - 0 ) !} (2 x)^{9} tan^{0} (7 x) : 512 x^{9}

化简

\frac{9 !}{1 ! ( 9 - 1 ) !} (2 x)^{8} tan^{1} (7 x) : 2304 x^{8} tan (7 x)

化简

\frac{9 !}{2 ! ( 9 - 2 ) !} (2 x)^{7} tan^{2} (7 x) : 4608 x^{7} tan^{2} (7 x)

化简

\frac{9 !}{3 ! ( 9 - 3 ) !} (2 x)^{6} tan^{3} (7 x) : 5376 x^{6} tan^{3} (7 x)

化简

\frac{9 !}{4 ! ( 9 - 4 ) !} (2 x)^{5} tan^{4} (7 x) : 4032 x^{5} tan^{4} (7 x)

化简

\frac{9 !}{5 ! ( 9 - 5 ) !} (2 x)^{4} tan^{5} (7 x) : 2016 x^{4} tan^{5} (7 x)

化简

\frac{9 !}{6 ! ( 9 - 6 ) !} (2 x)^{3} tan^{6} (7 x) : 672 x^{3} tan^{6} (7 x)

化简

\frac{9 !}{7 ! ( 9 - 7 ) !} (2 x)^{2} tan^{7} (7 x) : 144 x^{2} tan^{7} (7 x)

化简

\frac{9 !}{8 ! ( 9 - 8 ) !} (2 x)^{1} tan^{8} (7 x) : 18 x tan^{8} (7 x)

化简

\frac{9 !}{9 ! ( 9 - 9 ) !} (2 x)^{0} tan^{9} (7 x) : tan^{9} (7 x)

= 512 x^{9} + 2304 x^{8} tan (7 x) + 4608 x^{7} tan^{2} (7 x) + 5376 x^{6} tan^{3} (7 x) + 4032 x^{5} tan^{4} (7 x) + 2016 x^{4} tan^{5} (7 x) + 672 x^{3} tan^{6} (7 x) + 144 x^{2} tan^{7} (7 x) + 18 x tan^{8} (7 x) + tan^{9} (7 x)

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