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受欢迎的代数 >

展开 (c+1/c)^6

解答

展开

(c + \frac{1}{c})^{6}

解答

c^{6} + 6 c^{4} + 15 c^{2} + 20 + \frac{15}{c ^{2}} + \frac{6}{c ^{4}} + \frac{1}{c ^{6}}

求解步骤

(c + \frac{1}{c})^{6}

使用二项式定理:

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

a = c, b = \frac{1}{c}

= i = 0 \sum 6 (i 6) c^{(6 - i)} (\frac{1}{c})^{i}

展开求和

= \frac{6 !}{0 ! ( 6 - 0 ) !} c^{6} (\frac{1}{c})^{0} + \frac{6 !}{1 ! ( 6 - 1 ) !} c^{5} (\frac{1}{c})^{1} + \frac{6 !}{2 ! ( 6 - 2 ) !} c^{4} (\frac{1}{c})^{2} + \frac{6 !}{3 ! ( 6 - 3 ) !} c^{3} (\frac{1}{c})^{3} + \frac{6 !}{4 ! ( 6 - 4 ) !} c^{2} (\frac{1}{c})^{4} + \frac{6 !}{5 ! ( 6 - 5 ) !} c^{1} (\frac{1}{c})^{5} + \frac{6 !}{6 ! ( 6 - 6 ) !} c^{0} (\frac{1}{c})^{6}

化简

\frac{6 !}{0 ! ( 6 - 0 ) !} c^{6} (\frac{1}{c})^{0} : c^{6}

化简

\frac{6 !}{1 ! ( 6 - 1 ) !} c^{5} (\frac{1}{c})^{1} : 6 c^{4}

化简

\frac{6 !}{2 ! ( 6 - 2 ) !} c^{4} (\frac{1}{c})^{2} : 15 c^{2}

化简

\frac{6 !}{3 ! ( 6 - 3 ) !} c^{3} (\frac{1}{c})^{3} : 20

化简

\frac{6 !}{4 ! ( 6 - 4 ) !} c^{2} (\frac{1}{c})^{4} : \frac{15}{c ^{2}}

化简

\frac{6 !}{5 ! ( 6 - 5 ) !} c^{1} (\frac{1}{c})^{5} : \frac{6}{c ^{4}}

化简

\frac{6 !}{6 ! ( 6 - 6 ) !} c^{0} (\frac{1}{c})^{6} : \frac{1}{c ^{6}}

= c^{6} + 6 c^{4} + 15 c^{2} + 20 + \frac{15}{c ^{2}} + \frac{6}{c ^{4}} + \frac{1}{c ^{6}}

流行的例子

展开 2pi(r^3)

e x p an d 2 π (r^{3})

展开 100(2.2+7.5=133.56)

e x p an d 100 (2.2 + 7.5 = 133.56)

展开 (3x^2-t)/((x^2+t)^3)

e x p an d \frac{3 x ^{2} - t}{( x ^{2} + t ) ^{3}}

展开 (16pi(125-21sqrt(21)))/3

e x p an d \frac{16 π ( 125 - 21 21 )}{3}

d/(dt)((x(t,C))(1-1/(k*t*C)))

\frac{d}{d t} ((x (t, C)) (1 - \frac{1}{k \cdot t \cdot C}))