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受欢迎的代数 >

展开 (3-x/2)^6

解答

展开

(3 - \frac{x}{2})^{6}

解答

729 - 729 x + \frac{1215 x ^{2}}{4} - \frac{135 x ^{3}}{2} + \frac{135 x ^{4}}{16} - \frac{9 x ^{5}}{16} + \frac{x ^{6}}{64}

求解步骤

(3 - \frac{x}{2})^{6}

使用二项式定理:

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

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

= i = 0 \sum 6 (i 6) \cdot 3^{(6 - i)} (- \frac{x}{2})^{i}

展开求和

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

化简

\frac{6 !}{0 ! ( 6 - 0 ) !} \cdot 3^{6} (- \frac{x}{2})^{0} : 729

化简

\frac{6 !}{1 ! ( 6 - 1 ) !} \cdot 3^{5} (- \frac{x}{2})^{1} : - 729 x

化简

\frac{6 !}{2 ! ( 6 - 2 ) !} \cdot 3^{4} (- \frac{x}{2})^{2} : \frac{1215 x ^{2}}{4}

化简

\frac{6 !}{3 ! ( 6 - 3 ) !} \cdot 3^{3} (- \frac{x}{2})^{3} : - \frac{135 x ^{3}}{2}

化简

\frac{6 !}{4 ! ( 6 - 4 ) !} \cdot 3^{2} (- \frac{x}{2})^{4} : \frac{135 x ^{4}}{16}

化简

\frac{6 !}{5 ! ( 6 - 5 ) !} \cdot 3^{1} (- \frac{x}{2})^{5} : - \frac{9 x ^{5}}{16}

化简

\frac{6 !}{6 ! ( 6 - 6 ) !} \cdot 3^{0} (- \frac{x}{2})^{6} : \frac{x ^{6}}{64}

= 729 - 729 x + \frac{1215 x ^{2}}{4} - \frac{135 x ^{3}}{2} + \frac{135 x ^{4}}{16} - \frac{9 x ^{5}}{16} + \frac{x ^{6}}{64}

流行的例子

展开 (x^4-4x^3+2x^2-3x+1)/((x^2+1)^3)

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

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