Mister Exam
Factor -x^2-2*x*y-2*y^2 squared
The solution
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2 2 - x - 2*x*y - 2*y
$$- 2 y^{2} + \left(- x^{2} - 2 x y\right)$$
-x^2 - 2*x*y - 2*y^2
The perfect square
Let's highlight the perfect square of the square three-member
$$- 2 y^{2} + \left(- x^{2} - 2 x y\right)$$
Let us write down the identical expression
$$- 2 y^{2} + \left(- x^{2} - 2 x y\right) = - y^{2} + \left(- x^{2} - 2 x y - y^{2}\right)$$
or
$$- 2 y^{2} + \left(- x^{2} - 2 x y\right) = - y^{2} - \left(x + y\right)^{2}$$
$$- 2 y^{2} + \left(- x^{2} - 2 x y\right)$$
Let us write down the identical expression
$$- 2 y^{2} + \left(- x^{2} - 2 x y\right) = - y^{2} + \left(- x^{2} - 2 x y - y^{2}\right)$$
or
$$- 2 y^{2} + \left(- x^{2} - 2 x y\right) = - y^{2} - \left(x + y\right)^{2}$$
General simplification
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2 2 - x - 2*y - 2*x*y
$$- x^{2} - 2 x y - 2 y^{2}$$
-x^2 - 2*y^2 - 2*x*y
Factorization
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(x - y*(-1 + I))*(x + y*(1 + I))
$$\left(x - y \left(-1 + i\right)\right) \left(x + y \left(1 + i\right)\right)$$
(x - y*(-1 + i))*(x + y*(1 + i))
Combining rational expressions
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2 - 2*y + x*(-x - 2*y)
$$x \left(- x - 2 y\right) - 2 y^{2}$$
-2*y^2 + x*(-x - 2*y)