What is expand (a-sqrt(a^2-1))^3 ?

The solution to expand (a-sqrt(a^2-1))^3 is 4a^3-4a^2sqrt(a^2-1)-3a+sqrt(a^2-1)

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expand (a-sqrt(a^2-1))^3

expand

(a - a^{2} - 1)^{3}

4 a^{3} - 4 a^{2} a^{2} - 1 - 3 a + a^{2} - 1

Solution steps

(a - a^{2} - 1)^{3}

Apply Perfect Cube Formula:

(a - b)^{3} = a^{3} - 3 a^{2} b + 3 a b^{2} - b^{3}

(a - a^{2} - 1)^{3} = a^{3} - 3 a^{2} a^{2} - 1 + 3 a (a^{2} - 1)^{2} - (a^{2} - 1)^{3}

= a^{3} - 3 a^{2} a^{2} - 1 + 3 a (a^{2} - 1)^{2} - (a^{2} - 1)^{3}

Simplify

a^{3} - 3 a^{2} a^{2} - 1 + 3 a (a^{2} - 1)^{2} - (a^{2} - 1)^{3} : 4 a^{3} - 4 a^{2} a^{2} - 1 - 3 a + a^{2} - 1

= 4 a^{3} - 4 a^{2} a^{2} - 1 - 3 a + a^{2} - 1

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

\frac{x - x ln ( x )}{2} \cdot (- x)

(- 10 - 35) (7 + 821)

G (x, y, z) e n (1, - 5, 3)

What is expand (a-sqrt(a^2-1))^3 ?
The solution to expand (a-sqrt(a^2-1))^3 is 4a^3-4a^2sqrt(a^2-1)-3a+sqrt(a^2-1)