What is (a-sqrt(a^2-1))^2 ?

The solution to (a-sqrt(a^2-1))^2 is 2a^2-2asqrt(a^2-1)-1

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simplify (a-sqrt(a^2-1))^2

simplify

(a - a^{2} - 1)^{2}

2 a^{2} - 2 a a^{2} - 1 - 1

Solution steps

(a - a^{2} - 1)^{2}

Apply Perfect Square Formula:

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

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

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

Simplify

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

= 2 a^{2} - 2 a a^{2} - 1 - 1

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What is (a-sqrt(a^2-1))^2 ?
The solution to (a-sqrt(a^2-1))^2 is 2a^2-2asqrt(a^2-1)-1