What is 3x^2(x-2y)^2+9xy^2(2y-x) ?

The solution to 3x^2(x-2y)^2+9xy^2(2y-x) is 3x^4-12x^3y+3x^2y^2+18xy^3

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simplify 3x^2(x-2y)^2+9xy^2(2y-x)

simplify

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

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

Solution steps

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

Expand

3 x^{2} (x - 2 y)^{2} : 3 x^{4} - 12 x^{3} y + 12 x^{2} y^{2}

= 3 x^{4} - 12 x^{3} y + 12 x^{2} y^{2} + 9 x y^{2} (2 y - x)

Expand

9 x y^{2} (2 y - x) : 18 x y^{3} - 9 x^{2} y^{2}

= 3 x^{4} - 12 x^{3} y + 12 x^{2} y^{2} + 18 x y^{3} - 9 x^{2} y^{2}

Group like terms

= 3 x^{4} - 12 x^{3} y + 12 x^{2} y^{2} - 9 x^{2} y^{2} + 18 x y^{3}

Add similar elements:

12 x^{2} y^{2} - 9 x^{2} y^{2} = 3 x^{2} y^{2}

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

\frac{2}{2 + 7}

\frac{f}{7} < 21

x^{2} - x + 56 = 0

\frac{1}{5} + \frac{1}{4}

z^{2} + 13 z + 36

What is 3x^2(x-2y)^2+9xy^2(2y-x) ?
The solution to 3x^2(x-2y)^2+9xy^2(2y-x) is 3x^4-12x^3y+3x^2y^2+18xy^3