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

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

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factor xy(x-2y)+3y(2y-x)^2

factor

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

2 y (x - 2 y) (2 x - 3 y)

Solution steps

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

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

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

Factor out common term

y (x - 2 y) : y (x - 2 y) (x + 3 (x - 2 y))

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

Expand

x + 3 (x - 2 y) : 4 x - 6 y

= y (x - 2 y) (4 x - 6 y)

Factor

4 x - 6 y : 2 (2 x - 3 y)

= y (x - 2 y) \cdot 2 (2 x - 3 y)

= 2 y (x - 2 y) (2 x - 3 y)

t e^{- 2 t}

\frac{e}{i} = r

4 x^{2} - 9 x + 2

8 x^{6} + 27

x^{3} - 3 x^{2} + 9 x - 7

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