What is expand (y(y+1)^2)/2 ?

The solution to expand (y(y+1)^2)/2 is (y^3)/2+y^2+y/2

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expand (y(y+1)^2)/2

expand

\frac{y ( y + 1 ) ^{2}}{2}

\frac{y ^{3}}{2} + y^{2} + \frac{y}{2}

Solution steps

\frac{y ( y + 1 ) ^{2}}{2}

(y + 1)^{2} = y^{2} + 2 y + 1

= \frac{y ( y ^{2} + 2 y + 1 )}{2}

Expand

y (y^{2} + 2 y + 1) : y^{3} + 2 y^{2} + y

= \frac{y ^{3} + 2 y ^{2} + y}{2}

Apply the fraction rule:

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

\frac{y ^{3} + 2 y ^{2} + y}{2} = \frac{y ^{3}}{2} + \frac{2 y ^{2}}{2} + \frac{y}{2}

= \frac{y ^{3}}{2} + \frac{2 y ^{2}}{2} + \frac{y}{2}

Divide the numbers:

\frac{2}{2} = 1

= \frac{y ^{3}}{2} + y^{2} + \frac{y}{2}

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What is expand (y(y+1)^2)/2 ?
The solution to expand (y(y+1)^2)/2 is (y^3)/2+y^2+y/2