What is expand (sqrt((x+1)(x-1)))^3 ?

The solution to expand (sqrt((x+1)(x-1)))^3 is (x^2-1)^{3/2}

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expand (sqrt((x+1)(x-1)))^3

expand

((x + 1) (x - 1))^{3}

(x^{2} - 1)^{\frac{3}{2}}

Solution steps

((x + 1) (x - 1))^{3}

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

= (x^{2} - 1)^{3}

Apply radical rule:

a = a^{\frac{1}{2}}

= ((x^{2} - 1)^{\frac{1}{2}})^{3}

Apply exponent rule:

(a^{b})^{c} = a^{b c}

= (x^{2} - 1)^{\frac{1}{2} \cdot 3}

\frac{1}{2} \cdot 3 = \frac{3}{2}

= (x^{2} - 1)^{\frac{3}{2}}

\frac{( x ^{2} - 2 x - 15 ) ( x + 3 )}{( - x ^{2} - 1 )}

(3 x^{2} - 5 x - 4 \circ 2 x + 2) (3)

1 - 4.6277700000000 \dots^{- 15}

(5 sin (2 \frac{π}{4})) + 2 cos (2 \frac{π}{4})

\frac{1}{\frac{48.28 + x}{479.82 + 34.28 x}}

What is expand (sqrt((x+1)(x-1)))^3 ?
The solution to expand (sqrt((x+1)(x-1)))^3 is (x^2-1)^{3/2}