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受欢迎的代数 >

展开 (x+2/3)^5

解答

展开

(x + \frac{2}{3})^{5}

解答

x^{5} + \frac{10 x ^{4}}{3} + \frac{40 x ^{3}}{9} + \frac{80 x ^{2}}{27} + \frac{80 x}{81} + \frac{32}{243}

求解步骤

(x + \frac{2}{3})^{5}

使用二项式定理:

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

a = x, b = \frac{2}{3}

= i = 0 \sum 5 (i 5) x^{(5 - i)} (\frac{2}{3})^{i}

展开求和

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

化简

\frac{5 !}{0 ! ( 5 - 0 ) !} x^{5} (\frac{2}{3})^{0} : x^{5}

化简

\frac{5 !}{1 ! ( 5 - 1 ) !} x^{4} (\frac{2}{3})^{1} : \frac{10 x ^{4}}{3}

化简

\frac{5 !}{2 ! ( 5 - 2 ) !} x^{3} (\frac{2}{3})^{2} : \frac{40 x ^{3}}{9}

化简

\frac{5 !}{3 ! ( 5 - 3 ) !} x^{2} (\frac{2}{3})^{3} : \frac{80 x ^{2}}{27}

化简

\frac{5 !}{4 ! ( 5 - 4 ) !} x^{1} (\frac{2}{3})^{4} : \frac{80 x}{81}

化简

\frac{5 !}{5 ! ( 5 - 5 ) !} x^{0} (\frac{2}{3})^{5} : \frac{32}{243}

= x^{5} + \frac{10 x ^{4}}{3} + \frac{40 x ^{3}}{9} + \frac{80 x ^{2}}{27} + \frac{80 x}{81} + \frac{32}{243}

流行的例子

展开 (y^2-2xy)dx+x^2dy

e x p an d (y^{2} - 2 x y) d x + x^{2} d y

化简 (1+cos^2(x))(cos(x))

s im pl i f y (1 + cos^{2} (x)) (cos (x))

展开 (x^4+2y)dx-xdy

e x p an d (x^{4} + 2 y) d x - x d y

展开-1/3 P(-2,-3)

e x p an d - \frac{1}{3} P (- 2, - 3)

展开 e^x(5-x)

e x p an d e^{x} (5 - x)