Mister Exam
Factor -y^2-13*y*x-4*x^2 squared
The solution
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2 2 - y - 13*y*x - 4*x
$$- 4 x^{2} + \left(- x 13 y - y^{2}\right)$$
-y^2 - 13*y*x - 4*x^2
The perfect square
Let's highlight the perfect square of the square three-member
$$- 4 x^{2} + \left(- x 13 y - y^{2}\right)$$
Let us write down the identical expression
$$- 4 x^{2} + \left(- x 13 y - y^{2}\right) = \frac{153 y^{2}}{16} + \left(- 4 x^{2} - 13 x y - \frac{169 y^{2}}{16}\right)$$
or
$$- 4 x^{2} + \left(- x 13 y - y^{2}\right) = \frac{153 y^{2}}{16} - \left(2 x + \frac{13 y}{4}\right)^{2}$$
$$- 4 x^{2} + \left(- x 13 y - y^{2}\right)$$
Let us write down the identical expression
$$- 4 x^{2} + \left(- x 13 y - y^{2}\right) = \frac{153 y^{2}}{16} + \left(- 4 x^{2} - 13 x y - \frac{169 y^{2}}{16}\right)$$
or
$$- 4 x^{2} + \left(- x 13 y - y^{2}\right) = \frac{153 y^{2}}{16} - \left(2 x + \frac{13 y}{4}\right)^{2}$$
General simplification
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2 2 - y - 4*x - 13*x*y
$$- 4 x^{2} - 13 x y - y^{2}$$
-y^2 - 4*x^2 - 13*x*y
Factorization
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/ / ____\\ / / ____\\ | y*\-13 + 3*\/ 17 /| | y*\13 + 3*\/ 17 /| |x - ------------------|*|x + -----------------| \ 8 / \ 8 /
$$\left(x - \frac{y \left(-13 + 3 \sqrt{17}\right)}{8}\right) \left(x + \frac{y \left(3 \sqrt{17} + 13\right)}{8}\right)$$
(x - y*(-13 + 3*sqrt(17))/8)*(x + y*(13 + 3*sqrt(17))/8)
Assemble expression
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2 2 - y - 4*x - 13*x*y
$$- 4 x^{2} - 13 x y - y^{2}$$
-y^2 - 4*x^2 - 13*x*y
Trigonometric part
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2 2 - y - 4*x - 13*x*y
$$- 4 x^{2} - 13 x y - y^{2}$$
-y^2 - 4*x^2 - 13*x*y
Combining rational expressions
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2 - 4*x + y*(-y - 13*x)
$$- 4 x^{2} + y \left(- 13 x - y\right)$$
-4*x^2 + y*(-y - 13*x)
Rational denominator
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2 2 - y - 4*x - 13*x*y
$$- 4 x^{2} - 13 x y - y^{2}$$
-y^2 - 4*x^2 - 13*x*y
Common denominator
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2 2 - y - 4*x - 13*x*y
$$- 4 x^{2} - 13 x y - y^{2}$$
-y^2 - 4*x^2 - 13*x*y