What is expand (5y(-y+2)^3)/3 ?

The solution to expand (5y(-y+2)^3)/3 is -(5y^4)/3+10y^3-20y^2+(40y)/3

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expand (5y(-y+2)^3)/3

expand

\frac{5 y ( - y + 2 ) ^{3}}{3}

- \frac{5 y ^{4}}{3} + 10 y^{3} - 20 y^{2} + \frac{40 y}{3}

Solution steps

\frac{5 y ( - y + 2 ) ^{3}}{3}

(- y + 2)^{3} = - y^{3} + 6 y^{2} - 12 y + 8

= \frac{5 y ( - y ^{3} + 6 y ^{2} - 12 y + 8 )}{3}

Expand

5 y (- y^{3} + 6 y^{2} - 12 y + 8) : - 5 y^{4} + 30 y^{3} - 60 y^{2} + 40 y

= \frac{- 5 y ^{4} + 30 y ^{3} - 60 y ^{2} + 40 y}{3}

Apply the fraction rule:

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

\frac{- 5 y ^{4} + 30 y ^{3} - 60 y ^{2} + 40 y}{3} = - \frac{5 y ^{4}}{3} + \frac{30 y ^{3}}{3} - \frac{60 y ^{2}}{3} + \frac{40 y}{3}

= - \frac{5 y ^{4}}{3} + \frac{30 y ^{3}}{3} - \frac{60 y ^{2}}{3} + \frac{40 y}{3}

Divide the numbers:

\frac{30}{3} = 10

= - \frac{5 y ^{4}}{3} + 10 y^{3} - \frac{60 y ^{2}}{3} + \frac{40 y}{3}

Divide the numbers:

\frac{60}{3} = 20

= - \frac{5 y ^{4}}{3} + 10 y^{3} - 20 y^{2} + \frac{40 y}{3}

\frac{1}{( z ^{3} - 1 ) ( z ^{3} + 1 )}

\frac{28 ( 2 + 3 )}{5}

\frac{( k ( n + 1 ) ) !}{( kn ) !}

\frac{k}{x ( k - x )}

8 (y + 4) - 2 (y - 1 = 70 - 3 y)

What is expand (5y(-y+2)^3)/3 ?
The solution to expand (5y(-y+2)^3)/3 is -(5y^4)/3+10y^3-20y^2+(40y)/3