展开 1/((1+x+y+z)^3)

解答

展开

\frac{1}{( 1 + x + y + z ) ^{3}}

\frac{1}{x ^{3} + 3 x ^{2} y + 3 x ^{2} z + 3 x ^{2} + 3 x y ^{2} + 6 x y + 3 x z ^{2} + 6 x yz + 6 x z + 3 x + y ^{3} + 3 y ^{2} + 3 y + z ^{3} + 3 z ^{2} + 3 y z ^{2} + 6 yz + 3 y ^{2} z + 3 z + 1}

求解步骤

\frac{1}{( 1 + x + y + z ) ^{3}}

(1 + x + y + z)^{3} = x^{3} + 3 x^{2} y + 3 x^{2} z + 3 x^{2} + 3 x y^{2} + 6 x y + 3 x z^{2} + 6 x yz + 6 x z + 3 x + y^{3} + 3 y^{2} + 3 y + z^{3} + 3 z^{2} + 3 y z^{2} + 6 yz + 3 y^{2} z + 3 z + 1

= \frac{1}{x ^{3} + 3 x ^{2} y + 3 x ^{2} z + 3 x ^{2} + 3 x y ^{2} + 6 x y + 3 x z ^{2} + 6 x yz + 6 x z + 3 x + y ^{3} + 3 y ^{2} + 3 y + z ^{3} + 3 z ^{2} + 3 y z ^{2} + 6 yz + 3 y ^{2} z + 3 z + 1}

e x p an d \frac{ln ( x y ^{2} )}{( z )}

e x p an d f (x) (f (x) = 5 x + 6)

e x p an d y^{2} + (2 x + e^{y}) y y^{'} (x)

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

e x p an d \frac{( 5 x - 1 )}{( x + 1 ) ( x - 2 )}