What is (-w+sqrt(w^2-1))^2 ?

The solution to (-w+sqrt(w^2-1))^2 is 2w^2-2wsqrt(w^2-1)-1

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simplify (-w+sqrt(w^2-1))^2

simplify

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

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

Solution steps

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

Apply Perfect Square Formula:

(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}

Simplify

(- 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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What is (-w+sqrt(w^2-1))^2 ?
The solution to (-w+sqrt(w^2-1))^2 is 2w^2-2wsqrt(w^2-1)-1