展开 (2(x+5)(-x^2-10x+2))/((x^2+2)^3)

解答

展开

\frac{2 ( x + 5 ) ( - x ^{2} - 10 x + 2 )}{( x ^{2} + 2 ) ^{3}}

\frac{- 2 x ^{3} - 30 x ^{2} - 96 x + 20}{x ^{6} + 6 x ^{4} + 12 x ^{2} + 8}

求解步骤

\frac{2 ( x + 5 ) ( - x ^{2} - 10 x + 2 )}{( x ^{2} + 2 ) ^{3}}

(x^{2} + 2)^{3} = x^{6} + 6 x^{4} + 12 x^{2} + 8

= \frac{2 ( x + 5 ) ( - x ^{2} - 10 x + 2 )}{x ^{6} + 6 x ^{4} + 12 x ^{2} + 8}

乘开

2 (x + 5) (- x^{2} - 10 x + 2) : - 2 x^{3} - 30 x^{2} - 96 x + 20

= \frac{- 2 x ^{3} - 30 x ^{2} - 96 x + 20}{x ^{6} + 6 x ^{4} + 12 x ^{2} + 8}

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

s im pl i f y (4 x + 4)^{2}

s im pl i f y (- cot (x) csc (x)) (2 csc (x) - 1)

e x p an d (y + Δ)^{3}

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