What is expand (y''(x)(x^4-x)^5)/6 ?

The solution to expand (y''(x)(x^4-x)^5)/6 is

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expand (y''(x)(x^4-x)^5)/6

expand

\frac{y ^{''} ( x ) ( x ^{4} - x ) ^{5}}{6}

\frac{x ^{20} y '' ( x )}{6} - \frac{5 x ^{17} y '' ( x )}{6} + \frac{5 x ^{14} y '' ( x )}{3} - \frac{5 x ^{11} y '' ( x )}{3} + \frac{5 x ^{8} y '' ( x )}{6} - \frac{x ^{5} y '' ( x )}{6}

Solution steps

\frac{y ^{''} ( x ) ( x ^{4} - x ) ^{5}}{6}

(x^{4} - x)^{5} = x^{20} - 5 x^{17} + 10 x^{14} - 10 x^{11} + 5 x^{8} - x^{5}

= \frac{y ^{^{''}} ( x ) ( x ^{20} - 5 x ^{17} + 10 x ^{14} - 10 x ^{11} + 5 x ^{8} - x ^{5} )}{6}

Expand

y^{''} (x) (x^{20} - 5 x^{17} + 10 x^{14} - 10 x^{11} + 5 x^{8} - x^{5}) : x^{20} y^{''} (x) - 5 x^{17} y^{''} (x) + 10 x^{14} y^{''} (x) - 10 x^{11} y^{''} (x) + 5 x^{8} y^{''} (x) - x^{5} y^{''} (x)

= \frac{x ^{20} y ^{''} ( x ) - 5 x ^{17} y ^{''} ( x ) + 10 x ^{14} y ^{''} ( x ) - 10 x ^{11} y ^{''} ( x ) + 5 x ^{8} y ^{''} ( x ) - x ^{5} y ^{''} ( x )}{6}

Apply the fraction rule:

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

\frac{x ^{20} y ^{''} ( x ) - 5 x ^{17} y ^{''} ( x ) + 10 x ^{14} y ^{''} ( x ) - 10 x ^{11} y ^{''} ( x ) + 5 x ^{8} y ^{''} ( x ) - x ^{5} y ^{''} ( x )}{6} = \frac{x ^{20} y ^{''} ( x )}{6} - \frac{5 x ^{17} y ^{''} ( x )}{6} + \frac{10 x ^{14} y ^{''} ( x )}{6} - \frac{10 x ^{11} y ^{''} ( x )}{6} + \frac{5 x ^{8} y ^{''} ( x )}{6} - \frac{x ^{5} y ^{''} ( x )}{6}

= \frac{x ^{20} y ^{^{''}} ( x )}{6} - \frac{5 x ^{17} y ^{^{''}} ( x )}{6} + \frac{10 x ^{14} y ^{^{''}} ( x )}{6} - \frac{10 x ^{11} y ^{^{''}} ( x )}{6} + \frac{5 x ^{8} y ^{^{''}} ( x )}{6} - \frac{x ^{5} y ^{^{''}} ( x )}{6}

Cancel

\frac{10 x ^{14} y ^{''} ( x )}{6} : \frac{5 x ^{14} y ^{''} ( x )}{3}

= \frac{x ^{20} y ^{^{''}} ( x )}{6} - \frac{5 x ^{17} y ^{^{''}} ( x )}{6} + \frac{5 x ^{14} y ^{^{''}} ( x )}{3} - \frac{10 x ^{11} y ^{^{''}} ( x )}{6} + \frac{5 x ^{8} y ^{^{''}} ( x )}{6} - \frac{x ^{5} y ^{^{''}} ( x )}{6}

Cancel

\frac{10 x ^{11} y ^{''} ( x )}{6} : \frac{5 x ^{11} y ^{''} ( x )}{3}

= \frac{x ^{20} y ^{^{''}} ( x )}{6} - \frac{5 x ^{17} y ^{^{''}} ( x )}{6} + \frac{5 x ^{14} y ^{^{''}} ( x )}{3} - \frac{5 x ^{11} y ^{^{''}} ( x )}{3} + \frac{5 x ^{8} y ^{^{''}} ( x )}{6} - \frac{x ^{5} y ^{^{''}} ( x )}{6}

\frac{( 1 - x ) y}{x}

\frac{5 ( 9 + 21 )}{3}

(0.3 e^{- x} + 0.4 + 0.3 e^{x})^{2}

\frac{( 6 + x ) ^{2}}{36}

What is expand (y''(x)(x^4-x)^5)/6 ?
The solution to expand (y''(x)(x^4-x)^5)/6 is