What is expand (4t(-3t^5+5t^4)+15(t^4-t^2))/(30) ?

The solution to expand (4t(-3t^5+5t^4)+15(t^4-t^2))/(30) is -(2t^6)/5+(2t^5)/3+(t^4)/2-(t^2)/2

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expand (4t(-3t^5+5t^4)+15(t^4-t^2))/(30)

expand

\frac{4 t ( - 3 t ^{5} + 5 t ^{4} ) + 15 ( t ^{4} - t ^{2} )}{30}

- \frac{2 t ^{6}}{5} + \frac{2 t ^{5}}{3} + \frac{t ^{4}}{2} - \frac{t ^{2}}{2}

Solution steps

\frac{4 t ( - 3 t ^{5} + 5 t ^{4} ) + 15 ( t ^{4} - t ^{2} )}{30}

Expand

4 t (- 3 t^{5} + 5 t^{4}) + 15 (t^{4} - t^{2}) : - 12 t^{6} + 20 t^{5} + 15 t^{4} - 15 t^{2}

= \frac{- 12 t ^{6} + 20 t ^{5} + 15 t ^{4} - 15 t ^{2}}{30}

Apply the fraction rule:

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

\frac{- 12 t ^{6} + 20 t ^{5} + 15 t ^{4} - 15 t ^{2}}{30} = - \frac{12 t ^{6}}{30} + \frac{20 t ^{5}}{30} + \frac{15 t ^{4}}{30} - \frac{15 t ^{2}}{30}

= - \frac{12 t ^{6}}{30} + \frac{20 t ^{5}}{30} + \frac{15 t ^{4}}{30} - \frac{15 t ^{2}}{30}

\frac{12 t ^{6}}{30} = \frac{2 t ^{6}}{5}

\frac{20 t ^{5}}{30} = \frac{2 t ^{5}}{3}

\frac{15 t ^{4}}{30} = \frac{t ^{4}}{2}

\frac{15 t ^{2}}{30} = \frac{t ^{2}}{2}

= - \frac{2 t ^{6}}{5} + \frac{2 t ^{5}}{3} + \frac{t ^{4}}{2} - \frac{t ^{2}}{2}

((\frac{241363447}{129092883})^{\frac{1}{10}} - 1) \cdot 100

\frac{k ( s + 1 ) ( s + 2 ) ( s + 3 )}{s ^{3} ( s - 1 )}

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

\frac{( s - 1 ) ( s - 2 )}{( s + 1 ) ( s + 2 )}

(2 x y^{2} + 2 y) + (2 x^{2} y + 2 x) y^{'} (x)

What is expand (4t(-3t^5+5t^4)+15(t^4-t^2))/(30) ?
The solution to expand (4t(-3t^5+5t^4)+15(t^4-t^2))/(30) is -(2t^6)/5+(2t^5)/3+(t^4)/2-(t^2)/2