Mister Exam
Factor y^2+4*y*x-6*x^2 squared
The solution
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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 - \/ 10 /| | y*\2 + \/ 10 /| |x - --------------|*|x - --------------| \ 6 / \ 6 /
$$\left(x - \frac{y \left(2 - \sqrt{10}\right)}{6}\right) \left(x - \frac{y \left(2 + \sqrt{10}\right)}{6}\right)$$
(x - y*(2 - sqrt(10))/6)*(x - y*(2 + sqrt(10))/6)
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
$$- 6 x^{2} + \left(x 4 y + y^{2}\right) = \frac{5 y^{2}}{3} + \left(- 6 x^{2} + 4 x y - \frac{2 y^{2}}{3}\right)$$
or
$$- 6 x^{2} + \left(x 4 y + y^{2}\right) = \frac{5 y^{2}}{3} - \left(\sqrt{6} x - \frac{\sqrt{6} y}{3}\right)^{2}$$
$$- 6 x^{2} + \left(x 4 y + y^{2}\right)$$
Let us write down the identical expression
$$- 6 x^{2} + \left(x 4 y + y^{2}\right) = \frac{5 y^{2}}{3} + \left(- 6 x^{2} + 4 x y - \frac{2 y^{2}}{3}\right)$$
or
$$- 6 x^{2} + \left(x 4 y + y^{2}\right) = \frac{5 y^{2}}{3} - \left(\sqrt{6} x - \frac{\sqrt{6} y}{3}\right)^{2}$$
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)