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受欢迎的代数 >

展开 (1+sqrt(x))^7

解答

展开

(1 + x)^{7}

解答

1 + 7 x + 21 x + 35 x x + 35 x^{2} + 21 x^{2} x + 7 x^{3} + x^{3} x

求解步骤

(1 + x)^{7}

使用二项式定理:

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

a = 1, b = x

= i = 0 \sum 7 (i 7) \cdot 1^{(7 - i)} (x)^{i}

展开求和

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

化简

\frac{7 !}{0 ! ( 7 - 0 ) !} \cdot 1^{7} (x)^{0} : 1

化简

\frac{7 !}{1 ! ( 7 - 1 ) !} \cdot 1^{6} (x)^{1} : 7 x

化简

\frac{7 !}{2 ! ( 7 - 2 ) !} \cdot 1^{5} (x)^{2} : 21 x

化简

\frac{7 !}{3 ! ( 7 - 3 ) !} \cdot 1^{4} (x)^{3} : 35 (x)^{3}

化简

\frac{7 !}{4 ! ( 7 - 4 ) !} \cdot 1^{3} (x)^{4} : 35 x^{2}

化简

\frac{7 !}{5 ! ( 7 - 5 ) !} \cdot 1^{2} (x)^{5} : 21 (x)^{5}

化简

\frac{7 !}{6 ! ( 7 - 6 ) !} \cdot 1^{1} (x)^{6} : 7 x^{3}

化简

\frac{7 !}{7 ! ( 7 - 7 ) !} \cdot 1^{0} (x)^{7} : (x)^{7}

= 1 + 7 x + 21 x + 35 (x)^{3} + 35 x^{2} + 21 (x)^{5} + 7 x^{3} + (x)^{7}

(x)^{3} = x x

(x)^{5} = x^{2} x

(x)^{7} = x^{3} x

= 1 + 7 x + 21 x + 35 x x + 35 x^{2} + 21 x^{2} x + 7 x^{3} + x^{3} x

流行的例子

展开 (1+sqrt(x))^6

e x p an d (1 + x)^{6}

展开 (sqrt(2)(s^2+4))/(s^2+2)

e x p an d \frac{2 ( s ^{2} + 4 )}{s ^{2} + 2}

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e x p an d (x + 2) (x - 2) (x + \frac{17}{10}) (x - \frac{17}{10})

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e x p an d x 2 - 1.695 x + 0.2583

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e x p an d (9 + 3) (7 + 2)