Mister Exam
Factor -y^2+4*y*x-6*x^2 squared
The solution
You have entered
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2 2 - y + 4*y*x - 6*x
$$- 6 x^{2} + \left(x 4 y - y^{2}\right)$$
-y^2 + (4*y)*x - 6*x^2
Factorization
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/ / ___\\ / / ___\\ | y*\2 - I*\/ 2 /| | y*\2 + I*\/ 2 /| |x - ---------------|*|x - ---------------| \ 6 / \ 6 /
$$\left(x - \frac{y \left(2 - \sqrt{2} i\right)}{6}\right) \left(x - \frac{y \left(2 + \sqrt{2} i\right)}{6}\right)$$
(x - y*(2 - i*sqrt(2))/6)*(x - y*(2 + i*sqrt(2))/6)
General simplification
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2 2 - y - 6*x + 4*x*y
$$- 6 x^{2} + 4 x y - y^{2}$$
-y^2 - 6*x^2 + 4*x*y
The perfect square
Let's highlight the perfect square of the square three-member
$$- 6 x^{2} + \left(x 4 y - y^{2}\right)$$
Let us write down the identical expression
$$- 6 x^{2} + \left(x 4 y - y^{2}\right) = - \frac{y^{2}}{3} + \left(- 6 x^{2} + 4 x y - \frac{2 y^{2}}{3}\right)$$
or
$$- 6 x^{2} + \left(x 4 y - y^{2}\right) = - \frac{y^{2}}{3} - \left(\sqrt{6} x - \frac{\sqrt{6} y}{3}\right)^{2}$$
$$- 6 x^{2} + \left(x 4 y - y^{2}\right)$$
Let us write down the identical expression
$$- 6 x^{2} + \left(x 4 y - y^{2}\right) = - \frac{y^{2}}{3} + \left(- 6 x^{2} + 4 x y - \frac{2 y^{2}}{3}\right)$$
or
$$- 6 x^{2} + \left(x 4 y - y^{2}\right) = - \frac{y^{2}}{3} - \left(\sqrt{6} x - \frac{\sqrt{6} y}{3}\right)^{2}$$
Combining rational expressions
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2 - 6*x + y*(-y + 4*x)
$$- 6 x^{2} + y \left(4 x - y\right)$$
-6*x^2 + y*(-y + 4*x)