展开 (x+1/(x^2))^3

解答

展开

(x + \frac{1}{x ^{2}})^{3}

\frac{x ^{9} + 3 x ^{6} + 3 x ^{3} + 1}{x ^{6}}

求解步骤

(x + \frac{1}{x ^{2}})^{3}

使用完全立方公式:

(a + b)^{3} = a^{3} + 3 a^{2} b + 3 a b^{2} + b^{3}

(x + \frac{1}{x ^{2}})^{3} = x^{3} + 3 x^{2} \frac{1}{x ^{2}} + 3 x (\frac{1}{x ^{2}})^{2} + (\frac{1}{x ^{2}})^{3}

= x^{3} + 3 x^{2} \frac{1}{x ^{2}} + 3 x (\frac{1}{x ^{2}})^{2} + (\frac{1}{x ^{2}})^{3}

化简

x^{3} + 3 x^{2} \frac{1}{x ^{2}} + 3 x (\frac{1}{x ^{2}})^{2} + (\frac{1}{x ^{2}})^{3} : \frac{x ^{9} + 3 x ^{6} + 3 x ^{3} + 1}{x ^{6}}

= \frac{x ^{9} + 3 x ^{6} + 3 x ^{3} + 1}{x ^{6}}

e x p an d (5 cos (x) - cos (5 x)) (5 cos (x) - 5 cos (5 x))

e x p an d (- \frac{5}{6}, - \frac{3}{2}) y (\frac{11}{2}, \frac{1}{3})

e x p an d - 2 (x^{2} + 2Δ x^{2} + Δ^{2} x^{2}) + 1

e x p an d \frac{3 ( x ^{2} - x + 6 )}{4 ( x ^{2} - 9 )}

e x p an d \frac{3 ( 4 x ^{2} + 2 - 5 x )}{4}