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受欢迎的代数 >

展开 (x/3-y/2)^5

解答

展开

(\frac{x}{3} - \frac{y}{2})^{5}

解答

\frac{32 x ^{5} - 243 y ^{5}}{7776} - \frac{5 x ^{4} y}{162} + \frac{5 x ^{3} y ^{2}}{54} - \frac{5 x ^{2} y ^{3}}{36} + \frac{5 x y ^{4}}{48}

求解步骤

(\frac{x}{3} - \frac{y}{2})^{5}

使用二项式定理:

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

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

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

展开求和

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

化简

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

化简

\frac{5 !}{1 ! ( 5 - 1 ) !} (\frac{x}{3})^{4} (- \frac{y}{2})^{1} : - \frac{5 x ^{4} y}{162}

化简

\frac{5 !}{2 ! ( 5 - 2 ) !} (\frac{x}{3})^{3} (- \frac{y}{2})^{2} : \frac{5 x ^{3} y ^{2}}{54}

化简

\frac{5 !}{3 ! ( 5 - 3 ) !} (\frac{x}{3})^{2} (- \frac{y}{2})^{3} : - \frac{5 x ^{2} y ^{3}}{36}

化简

\frac{5 !}{4 ! ( 5 - 4 ) !} (\frac{x}{3})^{1} (- \frac{y}{2})^{4} : \frac{5 x y ^{4}}{48}

化简

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

= \frac{x ^{5}}{243} - \frac{5 x ^{4} y}{162} + \frac{5 x ^{3} y ^{2}}{54} - \frac{5 x ^{2} y ^{3}}{36} + \frac{5 x y ^{4}}{48} - \frac{y ^{5}}{32}

化简

\frac{x ^{5}}{243} - \frac{5 x ^{4} y}{162} + \frac{5 x ^{3} y ^{2}}{54} - \frac{5 x ^{2} y ^{3}}{36} + \frac{5 x y ^{4}}{48} - \frac{y ^{5}}{32} : \frac{32 x ^{5} - 243 y ^{5}}{7776} - \frac{5 x ^{4} y}{162} + \frac{5 x ^{3} y ^{2}}{54} - \frac{5 x ^{2} y ^{3}}{36} + \frac{5 x y ^{4}}{48}

= \frac{32 x ^{5} - 243 y ^{5}}{7776} - \frac{5 x ^{4} y}{162} + \frac{5 x ^{3} y ^{2}}{54} - \frac{5 x ^{2} y ^{3}}{36} + \frac{5 x y ^{4}}{48}

流行的例子

展开 (2(y-x)-1-1-(y-x))left(x,1,-y)

e x p an d (2 (y - x) - 1 - 1 - (y - x)) l e f t (x, 1, - y)

展开 ((x+2)(x+1))/((x-1)(x-3))

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

展开 (x-5)/((x+1)(x-1))

e x p an d \frac{x - 5}{( x + 1 ) ( x - 1 )}

展开 1/((1-x)(1+x))

e x p an d \frac{1}{( 1 - x ) ( 1 + x )}

化简 (sqrt(2x+1)-3)^2

s im pl i f y (2 x + 1 - 3)^{2}