Mister Exam
Factor -y^2+8*y*x-8*x^2 squared
The solution
You have entered
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2 2 - y + 8*y*x - 8*x
$$- 8 x^{2} + \left(x 8 y - y^{2}\right)$$
-y^2 + (8*y)*x - 8*x^2
Factorization
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/ / ___\\ / / ___\\ | y*\2 - \/ 2 /| | y*\2 + \/ 2 /| |x - -------------|*|x - -------------| \ 4 / \ 4 /
$$\left(x - \frac{y \left(2 - \sqrt{2}\right)}{4}\right) \left(x - \frac{y \left(\sqrt{2} + 2\right)}{4}\right)$$
(x - y*(2 - sqrt(2))/4)*(x - y*(2 + sqrt(2))/4)
The perfect square
Let's highlight the perfect square of the square three-member
$$- 8 x^{2} + \left(x 8 y - y^{2}\right)$$
Let us write down the identical expression
$$- 8 x^{2} + \left(x 8 y - y^{2}\right) = y^{2} + \left(- 8 x^{2} + 8 x y - 2 y^{2}\right)$$
or
$$- 8 x^{2} + \left(x 8 y - y^{2}\right) = y^{2} - \left(2 \sqrt{2} x - \sqrt{2} y\right)^{2}$$
$$- 8 x^{2} + \left(x 8 y - y^{2}\right)$$
Let us write down the identical expression
$$- 8 x^{2} + \left(x 8 y - y^{2}\right) = y^{2} + \left(- 8 x^{2} + 8 x y - 2 y^{2}\right)$$
or
$$- 8 x^{2} + \left(x 8 y - y^{2}\right) = y^{2} - \left(2 \sqrt{2} x - \sqrt{2} y\right)^{2}$$
General simplification
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2 2 - y - 8*x + 8*x*y
$$- 8 x^{2} + 8 x y - y^{2}$$
-y^2 - 8*x^2 + 8*x*y
Combining rational expressions
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2 - 8*x + y*(-y + 8*x)
$$- 8 x^{2} + y \left(8 x - y\right)$$
-8*x^2 + y*(-y + 8*x)