化简 (-w+sqrt(w^2-1))^2

解答

化简

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

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

求解步骤

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

使用完全平方公式:

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

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

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

化简

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

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

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