What is v(((1+v^2)^5)/5-v^9) ?

The solution to v(((1+v^2)^5)/5-v^9) is (v(-5v^9+1+5v^2+10v^4+10v^6+5v^8+v^{10}))/5

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simplify v(((1+v^2)^5)/5-v^9)

simplify

v (\frac{( 1 + v ^{2} ) ^{5}}{5} - v^{9})

\frac{v ( - 5 v ^{9} + 1 + 5 v ^{2} + 10 v ^{4} + 10 v ^{6} + 5 v ^{8} + v ^{10} )}{5}

Solution steps

v (\frac{( 1 + v ^{2} ) ^{5}}{5} - v^{9})

Join

\frac{( 1 + v ^{2} ) ^{5}}{5} - v^{9} : \frac{- 5 v ^{9} + 1 + 5 v ^{2} + 10 v ^{4} + 10 v ^{6} + 5 v ^{8} + v ^{10}}{5}

= v \frac{- 5 v ^{9} + 1 + 5 v ^{2} + 10 v ^{4} + 10 v ^{6} + 5 v ^{8} + v ^{10}}{5}

Apply the fraction rule:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

= \frac{v ( - 5 v ^{9} + 1 + 5 v ^{2} + 10 v ^{4} + 10 v ^{6} + 5 v ^{8} + v ^{10} )}{5}

\frac{x y \cdot ( 32 - x y )}{( x + y )}

3 (t - \frac{π}{4})

(x^{2}) (x^{3} - 5 e^{- 2 x} - 2 x^{\frac{1}{2}})

(1 + a) (1 - a)

\frac{d}{d x} ((1 - x) e^{x}) - 1

What is v(((1+v^2)^5)/5-v^9) ?
The solution to v(((1+v^2)^5)/5-v^9) is (v(-5v^9+1+5v^2+10v^4+10v^6+5v^8+v^{10}))/5