展开 (1-w+sqrt(w^2-1))^2

解答

展开

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

2 w^{2} - 2 w + 2 w^{2} - 1 - 2 w w^{2} - 1

求解步骤

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

使用指数法则:

a^{b + c} = a^{b} \cdot a^{c}

(1 - w + w^{2} - 1)^{2} = (1 - w + w^{2} - 1) (1 - w + w^{2} - 1)

= (1 - w + w^{2} - 1) (1 - w + w^{2} - 1)

打开括号

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

化简

1 \cdot 1 + 1 \cdot (- w) + 1 \cdot w^{2} - 1 - w \cdot 1 - w (- w) - w w^{2} - 1 + w^{2} - 1 \cdot 1 + w^{2} - 1 (- w) + w^{2} - 1 w^{2} - 1 : 2 w^{2} - 2 w + 2 w^{2} - 1 - 2 w w^{2} - 1

= 2 w^{2} - 2 w + 2 w^{2} - 1 - 2 w w^{2} - 1

e x p an d \frac{( x + 1 ) ( x - 1 ) ( x - 2 ) ( x - 3 )}{6}

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

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

e x p an d ((2 + cos (u) sin (u)))^{2}

e x p an d \frac{10 x + 9}{3 ( x + 1 ) ( 2 x + 3 )}