What is expand (1-x^2)(L((1-x^2)^{(m^2)/2}-m^2x^2(1-x^2)^{(m^2)/2-1})) ?

The solution to expand (1-x^2)(L((1-x^2)^{(m^2)/2}-m^2x^2(1-x^2)^{(m^2)/2-1})) is

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expand (1-x^2)(L((1-x^2)^{(m^2)/2}-m^2x^2(1-x^2)^{(m^2)/2-1}))

expand

(1 - x^{2}) (L ((1 - x^{2})^{\frac{m ^{2}}{2}} - m^{2} x^{2} (1 - x^{2})^{\frac{m ^{2}}{2} - 1}))

1 \cdot (L ((1 - x^{2})^{\frac{m ^{2}}{2}} - m^{2} x^{2} (1 - x^{2})^{\frac{m ^{2}}{2} - 1})) - x^{2} (L ((1 - x^{2})^{\frac{m ^{2}}{2}} - m^{2} x^{2} (1 - x^{2})^{\frac{m ^{2}}{2} - 1}))

Solution steps

(1 - x^{2}) (L ((1 - x^{2})^{\frac{m ^{2}}{2}} - m^{2} x^{2} (1 - x^{2})^{\frac{m ^{2}}{2} - 1}))

Apply the distributive law:

a (b - c) = ab - a c

a = (L ((1 - x^{2})^{\frac{m ^{2}}{2}} - m^{2} x^{2} (1 - x^{2})^{\frac{m ^{2}}{2} - 1})), b = 1, c = x^{2}

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

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

(2 - sin^{2} (x)) (cos^{2} (x))

\frac{x + 2}{x ( x - 6 )}

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

sin ((1 - n) π)

\frac{32 x ^{3} - 204 x ^{2}}{( 4 x - 17 ) ^{2}}

What is expand (1-x^2)(L((1-x^2)^{(m^2)/2}-m^2x^2(1-x^2)^{(m^2)/2-1})) ?
The solution to expand (1-x^2)(L((1-x^2)^{(m^2)/2}-m^2x^2(1-x^2)^{(m^2)/2-1})) is