What is xy(x-3y)-x(y^2-3x)-y(x^2-y) ?

The solution to xy(x-3y)-x(y^2-3x)-y(x^2-y) is 3x^2-4xy^2+y^2

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simplify xy(x-3y)-x(y^2-3x)-y(x^2-y)

simplify

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

3 x^{2} - 4 x y^{2} + y^{2}

Solution steps

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

Expand

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

= x^{2} y - 3 x y^{2} - x (y^{2} - 3 x) - y (x^{2} - y)

Expand

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

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

Expand

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

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

Add similar elements:

- 3 x y^{2} - x y^{2} = - 4 x y^{2}

= x^{2} y - 4 x y^{2} + 3 x^{2} - x^{2} y + y^{2}

Group like terms

= x^{2} y - x^{2} y + 3 x^{2} - 4 x y^{2} + y^{2}

Add similar elements:

x^{2} y - x^{2} y = 0

= 3 x^{2} - 4 x y^{2} + y^{2}

\frac{2 x ^{2} - 5 x}{x}

1 - a^{4}

(h + 1)^{3}

\frac{1}{2} \cdot \frac{1}{2}

\frac{1}{1 + e ^{- 0}}

What is xy(x-3y)-x(y^2-3x)-y(x^2-y) ?
The solution to xy(x-3y)-x(y^2-3x)-y(x^2-y) is 3x^2-4xy^2+y^2