Mister Exam
Factor -x^2+12*x*y-2*y^2 squared
The solution
You have entered
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2 2 - x + 12*x*y - 2*y
$$- 2 y^{2} + \left(- x^{2} + 12 x y\right)$$
-x^2 + (12*x)*y - 2*y^2
General simplification
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2 2 - x - 2*y + 12*x*y
$$- x^{2} + 12 x y - 2 y^{2}$$
-x^2 - 2*y^2 + 12*x*y
Factorization
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/ / ____\\ / / ____\\ \x - y*\6 - \/ 34 //*\x - y*\6 + \/ 34 //
$$\left(x - y \left(6 - \sqrt{34}\right)\right) \left(x - y \left(\sqrt{34} + 6\right)\right)$$
(x - y*(6 - sqrt(34)))*(x - y*(6 + sqrt(34)))
The perfect square
Let's highlight the perfect square of the square three-member
$$- 2 y^{2} + \left(- x^{2} + 12 x y\right)$$
Let us write down the identical expression
$$- 2 y^{2} + \left(- x^{2} + 12 x y\right) = 34 y^{2} + \left(- x^{2} + 12 x y - 36 y^{2}\right)$$
or
$$- 2 y^{2} + \left(- x^{2} + 12 x y\right) = 34 y^{2} - \left(x - 6 y\right)^{2}$$
$$- 2 y^{2} + \left(- x^{2} + 12 x y\right)$$
Let us write down the identical expression
$$- 2 y^{2} + \left(- x^{2} + 12 x y\right) = 34 y^{2} + \left(- x^{2} + 12 x y - 36 y^{2}\right)$$
or
$$- 2 y^{2} + \left(- x^{2} + 12 x y\right) = 34 y^{2} - \left(x - 6 y\right)^{2}$$
Common denominator
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2 2 - x - 2*y + 12*x*y
$$- x^{2} + 12 x y - 2 y^{2}$$
-x^2 - 2*y^2 + 12*x*y
Assemble expression
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2 2 - x - 2*y + 12*x*y
$$- x^{2} + 12 x y - 2 y^{2}$$
-x^2 - 2*y^2 + 12*x*y
Rational denominator
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2 2 - x - 2*y + 12*x*y
$$- x^{2} + 12 x y - 2 y^{2}$$
-x^2 - 2*y^2 + 12*x*y
Combining rational expressions
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2 - 2*y + x*(-x + 12*y)
$$x \left(- x + 12 y\right) - 2 y^{2}$$
-2*y^2 + x*(-x + 12*y)
Trigonometric part
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2 2 - x - 2*y + 12*x*y
$$- x^{2} + 12 x y - 2 y^{2}$$
-x^2 - 2*y^2 + 12*x*y