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

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

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expand x(1-x-y)^2

expand

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

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

Solution steps

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

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

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

Distribute parentheses

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

Apply minus-plus rules

+ (- a) = - a

= 2 xx y - 2 xx + x^{2} x - 2 x y + x y^{2} + 1 \cdot x

Simplify

2 xx y - 2 xx + x^{2} x - 2 x y + x y^{2} + 1 \cdot x : 2 x^{2} y - 2 x^{2} + x^{3} - 2 x y + x y^{2} + x

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

(12 y + 2 t - 5) d t + (6 y + 12 t - 1) d y

(3 (x - 2 y) + 2 (x + 3) = 4,) (4 (x + y) - 3 (x + 2 y) = - 2)

(4 x + 5) (x ln (x) - x)

e^{t - 2} U (t - 2)

\frac{x ^{5} + 1}{( x ^{2} - x ) ( x ^{4} + 2 x ^{2} + 1 )}

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