What is expand-(y(y-3)^4)/2 ?

The solution to expand-(y(y-3)^4)/2 is -(y^5)/2+6y^4-27y^3+54y^2-(81y)/2

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expand-(y(y-3)^4)/2

expand

- \frac{y ( y - 3 ) ^{4}}{2}

- \frac{y ^{5}}{2} + 6 y^{4} - 27 y^{3} + 54 y^{2} - \frac{81 y}{2}

Solution steps

- \frac{y ( y - 3 ) ^{4}}{2}

(y - 3)^{4} = y^{4} - 12 y^{3} + 54 y^{2} - 108 y + 81

= - \frac{y ( y ^{4} - 12 y ^{3} + 54 y ^{2} - 108 y + 81 )}{2}

Expand

y (y^{4} - 12 y^{3} + 54 y^{2} - 108 y + 81) : y^{5} - 12 y^{4} + 54 y^{3} - 108 y^{2} + 81 y

= - \frac{y ^{5} - 12 y ^{4} + 54 y ^{3} - 108 y ^{2} + 81 y}{2}

Apply the fraction rule:

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

\frac{y ^{5} - 12 y ^{4} + 54 y ^{3} - 108 y ^{2} + 81 y}{2} = - (\frac{y ^{5}}{2}) - (- \frac{12 y ^{4}}{2}) - (\frac{54 y ^{3}}{2}) - (- \frac{108 y ^{2}}{2}) - (\frac{81 y}{2})

= - (\frac{y ^{5}}{2}) - (- \frac{12 y ^{4}}{2}) - (\frac{54 y ^{3}}{2}) - (- \frac{108 y ^{2}}{2}) - (\frac{81 y}{2})

Remove parentheses:

(a) = a, - (- a) = a

= - \frac{y ^{5}}{2} + \frac{12 y ^{4}}{2} - \frac{54 y ^{3}}{2} + \frac{108 y ^{2}}{2} - \frac{81 y}{2}

Divide the numbers:

\frac{12}{2} = 6

= - \frac{y ^{5}}{2} + 6 y^{4} - \frac{54 y ^{3}}{2} + \frac{108 y ^{2}}{2} - \frac{81 y}{2}

Divide the numbers:

\frac{54}{2} = 27

= - \frac{y ^{5}}{2} + 6 y^{4} - 27 y^{3} + \frac{108 y ^{2}}{2} - \frac{81 y}{2}

Divide the numbers:

\frac{108}{2} = 54

= - \frac{y ^{5}}{2} + 6 y^{4} - 27 y^{3} + 54 y^{2} - \frac{81 y}{2}

\frac{q ( d - x ) ^{2}}{x ^{2}}

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

- \frac{4 x ^{2} - 41 x + 104}{( x - 4 ) ^{3}}

- (4 i - 4) \pm (4 i - 4)^{2} - 4 (1 - i) (3 - 11 i)

(\frac{x - 4}{2} + \frac{y}{1} - 2 = 0) 2

What is expand-(y(y-3)^4)/2 ?
The solution to expand-(y(y-3)^4)/2 is -(y^5)/2+6y^4-27y^3+54y^2-(81y)/2