化简 (z^2-1)(z^2-sqrt(2)+1)(z^2+1)(z^2+sqrt(2)+1)

解答

化简

(z^{2} - 1) (z^{2} - 2 + 1) (z^{2} + 1) (z^{2} + 2 + 1)

(z^{2} - 1) (z^{4} + 2 z^{2} - 1) (z^{2} + 1)

求解步骤

(z^{2} - 1) (z^{2} - 2 + 1) (z^{2} + 1) (z^{2} + 2 + 1)

打开括号

= (z^{2} - 1) (z^{2} z^{2} + z^{2} 2 + z^{2} \cdot 1 - 2 z^{2} - 22 - 2 \cdot 1 + 1 \cdot z^{2} + 1 \cdot 2 + 1 \cdot 1) (z^{2} + 1)

化简

z^{2} z^{2} + z^{2} 2 + z^{2} \cdot 1 - 2 z^{2} - 22 - 2 \cdot 1 + 1 \cdot z^{2} + 1 \cdot 2 + 1 \cdot 1 : z^{4} + 2 z^{2} - 1

= (z^{2} - 1) (z^{4} + 2 z^{2} - 1) (z^{2} + 1)

e x p an d \frac{2 ln ( 3 )}{5 ( - e ^{\frac{l n ( 3 )}{20}} + 1 )}

s im pl i f y (x + \frac{3}{5}) (x - \frac{2}{5})

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

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

so l v e f or f, f = x \cdot e^{- x} + δ (x - 4)