What is expand (y(1-x-y)^2)/2 ?

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

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expand (y(1-x-y)^2)/2

expand

\frac{y ( 1 - x - y ) ^{2}}{2}

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

Solution steps

\frac{y ( 1 - x - y ) ^{2}}{2}

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

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

Expand

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

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

Apply the fraction rule:

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

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

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

Divide the numbers:

\frac{2}{2} = 1

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

0.5 8^{2}

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

(2 x - 5 y) e^{3}

- 7 (x)

2 (2 t e^{t} + e^{t})

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