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受欢迎的代数 >

展开 (2+x/2)^8

解答

展开

(2 + \frac{x}{2})^{8}

解答

256 + 512 x + 448 x^{2} + 224 x^{3} + 70 x^{4} + 14 x^{5} + \frac{7 x ^{6}}{4} + \frac{x ^{7}}{8} + \frac{x ^{8}}{256}

求解步骤

(2 + \frac{x}{2})^{8}

使用二项式定理:

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

a = 2, b = \frac{x}{2}

= i = 0 \sum 8 (i 8) \cdot 2^{(8 - i)} (\frac{x}{2})^{i}

展开求和

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

化简

\frac{8 !}{0 ! ( 8 - 0 ) !} \cdot 2^{8} (\frac{x}{2})^{0} : 256

化简

\frac{8 !}{1 ! ( 8 - 1 ) !} \cdot 2^{7} (\frac{x}{2})^{1} : 512 x

化简

\frac{8 !}{2 ! ( 8 - 2 ) !} \cdot 2^{6} (\frac{x}{2})^{2} : 448 x^{2}

化简

\frac{8 !}{3 ! ( 8 - 3 ) !} \cdot 2^{5} (\frac{x}{2})^{3} : 224 x^{3}

化简

\frac{8 !}{4 ! ( 8 - 4 ) !} \cdot 2^{4} (\frac{x}{2})^{4} : 70 x^{4}

化简

\frac{8 !}{5 ! ( 8 - 5 ) !} \cdot 2^{3} (\frac{x}{2})^{5} : 14 x^{5}

化简

\frac{8 !}{6 ! ( 8 - 6 ) !} \cdot 2^{2} (\frac{x}{2})^{6} : \frac{7 x ^{6}}{4}

化简

\frac{8 !}{7 ! ( 8 - 7 ) !} \cdot 2^{1} (\frac{x}{2})^{7} : \frac{x ^{7}}{8}

化简

\frac{8 !}{8 ! ( 8 - 8 ) !} \cdot 2^{0} (\frac{x}{2})^{8} : \frac{x ^{8}}{256}

= 256 + 512 x + 448 x^{2} + 224 x^{3} + 70 x^{4} + 14 x^{5} + \frac{7 x ^{6}}{4} + \frac{x ^{7}}{8} + \frac{x ^{8}}{256}

流行的例子

化简 (x-sqrt(6))^2

s im pl i f y (x - 6)^{2}

展开 (3x^2-4)(x^3-4x)^{1/2}

e x p an d (3 x^{2} - 4) (x^{3} - 4 x)^{\frac{1}{2}}

化简 (sqrt(a)-2sqrt(x))*(3sqrt(a)+sqrt(x))

s im pl i f y (a - 2 x) \cdot (3 a + x)

展开-sin(x)*(sin(x)-k)

e x p an d - sin (x) \cdot (sin (x) - k)

展开 ((3s^2+20))/(((s+4)s^2+1))

e x p an d \frac{( 3 s ^{2} + 20 )}{( ( s + 4 ) s ^{2} + 1 )}