What is expand sqrt(1+x^2)(x^2-1) ?

The solution to expand sqrt(1+x^2)(x^2-1) is x^2sqrt(1+x^2)-sqrt(1+x^2)

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expand sqrt(1+x^2)(x^2-1)

expand

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

x^{2} 1 + x^{2} - 1 + x^{2}

Solution steps

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

Apply the distributive law:

a (b - c) = ab - a c

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

= 1 + x^{2} x^{2} - 1 + x^{2} \cdot 1

Simplify

1 + x^{2} x^{2} - 1 + x^{2} \cdot 1 : x^{2} 1 + x^{2} - 1 + x^{2}

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

- \frac{16 ( 8 - 3 x ^{2} )}{( x ^{2} + 8 ) ^{3}}

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

\frac{21937.5}{20000}

\frac{k ( k - 1 ) ( k + 1 )}{3}

(3 + sin (4 θ))^{2}

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