What is expand 2xy(3y-x-1)^2 ?

The solution to expand 2xy(3y-x-1)^2 is -12x^2y^2+2x^3y+4x^2y+18xy^3-12xy^2+2xy

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expand 2xy(3y-x-1)^2

expand

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

- 12 x^{2} y^{2} + 2 x^{3} y + 4 x^{2} y + 18 x y^{3} - 12 x y^{2} + 2 x y

Solution steps

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

(3 y - x - 1)^{2} = - 6 x y + x^{2} + 2 x + 9 y^{2} - 6 y + 1

= 2 x y (x^{2} + 2 x - 6 x y + 9 y^{2} + 1 - 6 y)

Distribute parentheses

= 2 x y (- 6 x y) + 2 x y x^{2} + 2 x y \cdot 2 x + 2 x y \cdot 9 y^{2} + 2 x y (- 6 y) + 2 x y \cdot 1

Apply minus-plus rules

+ (- a) = - a

= - 2 \cdot 6 xx yy + 2 x^{2} x y + 2 \cdot 2 xx y + 2 \cdot 9 x y^{2} y - 2 \cdot 6 x yy + 2 \cdot 1 \cdot x y

Simplify

- 2 \cdot 6 xx yy + 2 x^{2} x y + 2 \cdot 2 xx y + 2 \cdot 9 x y^{2} y - 2 \cdot 6 x yy + 2 \cdot 1 \cdot x y : - 12 x^{2} y^{2} + 2 x^{3} y + 4 x^{2} y + 18 x y^{3} - 12 x y^{2} + 2 x y

= - 12 x^{2} y^{2} + 2 x^{3} y + 4 x^{2} y + 18 x y^{3} - 12 x y^{2} + 2 x y

3!

1.732 - 1661

x sin (y) (1 - x)

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

x sin (y) d y + (x^{3} - 2 x^{2} cos (y) + cos (y)) d y

What is expand 2xy(3y-x-1)^2 ?
The solution to expand 2xy(3y-x-1)^2 is -12x^2y^2+2x^3y+4x^2y+18xy^3-12xy^2+2xy