#160; x(x + y)^3 3x^3y (x + y) ⇒ x (x^3 + y^3+3x^2y +3xy^2) 3x^3y (x + y) ⇒ x^4 + xy^3y +3x^2y + 3x^2y^2 3x^4y 3x^3y^2 ...

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Solving a Quadratic Equation by Completion of Squares Method

Solve: xx+y3...

Question

Solve:
$x (x + y)^{3} - 3 x^{3} y (x + y)$

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Solution

$x (x + y)^{3} - 3 x^{3} y (x + y)$
$\Rightarrow x (x^{3} + y^{3} + 3 x^{2} y + 3 x y^{2}) - 3 x^{3} y (x + y)$
$\Rightarrow x^{4} + x y^{3} y + 3 x^{2} y + 3 x^{2} y^{2} - 3 x^{4} y - 3 x^{3} y^{2}$

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