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受欢迎的代数 >

展开 (1/2-x^2)^7

解答

展开

(\frac{1}{2} - x^{2})^{7}

解答

\frac{1}{128} - \frac{7 x ^{2}}{64} + \frac{21 x ^{4}}{32} - \frac{35 x ^{6}}{16} + \frac{35 x ^{8}}{8} - \frac{21 x ^{10}}{4} + \frac{7 x ^{12}}{2} - x^{14}

求解步骤

(\frac{1}{2} - x^{2})^{7}

使用二项式定理:

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

a = \frac{1}{2}, b = - x^{2}

= i = 0 \sum 7 (i 7) (\frac{1}{2})^{(7 - i)} (- x^{2})^{i}

展开求和

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

化简

\frac{7 !}{0 ! ( 7 - 0 ) !} (\frac{1}{2})^{7} (- x^{2})^{0} : \frac{1}{128}

化简

\frac{7 !}{1 ! ( 7 - 1 ) !} (\frac{1}{2})^{6} (- x^{2})^{1} : - \frac{7 x ^{2}}{64}

化简

\frac{7 !}{2 ! ( 7 - 2 ) !} (\frac{1}{2})^{5} (- x^{2})^{2} : \frac{21 x ^{4}}{32}

化简

\frac{7 !}{3 ! ( 7 - 3 ) !} (\frac{1}{2})^{4} (- x^{2})^{3} : - \frac{35 x ^{6}}{16}

化简

\frac{7 !}{4 ! ( 7 - 4 ) !} (\frac{1}{2})^{3} (- x^{2})^{4} : \frac{35 x ^{8}}{8}

化简

\frac{7 !}{5 ! ( 7 - 5 ) !} (\frac{1}{2})^{2} (- x^{2})^{5} : - \frac{21 x ^{10}}{4}

化简

\frac{7 !}{6 ! ( 7 - 6 ) !} (\frac{1}{2})^{1} (- x^{2})^{6} : \frac{7 x ^{12}}{2}

化简

\frac{7 !}{7 ! ( 7 - 7 ) !} (\frac{1}{2})^{0} (- x^{2})^{7} : - x^{14}

= \frac{1}{128} - \frac{7 x ^{2}}{64} + \frac{21 x ^{4}}{32} - \frac{35 x ^{6}}{16} + \frac{35 x ^{8}}{8} - \frac{21 x ^{10}}{4} + \frac{7 x ^{12}}{2} - x^{14}

流行的例子

展开 1/(2(1-x))

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

展开 (1/2-x^2)^4

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

展开 x(x+Δx)

e x p an d x (x + Δ x)

化简 1+(k(0.3679z+0.2642))/((z-0.3679)(z-1))

s im pl i f y 1 + \frac{k ( 0.3679 z + 0.2642 )}{( z - 0.3679 ) ( z - 1 )}

展开 (y-x^3)dx+(y^3+x)dy

e x p an d (y - x^{3}) d x + (y^{3} + x) d y