Mister Exam
Factor -y^2-7*y*x-15*x^2 squared
The solution
You have entered
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2 2 - y - 7*y*x - 15*x
$$- 15 x^{2} + \left(- x 7 y - y^{2}\right)$$
-y^2 - 7*y*x - 15*x^2
General simplification
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2 2 - y - 15*x - 7*x*y
$$- 15 x^{2} - 7 x y - y^{2}$$
-y^2 - 15*x^2 - 7*x*y
The perfect square
Let's highlight the perfect square of the square three-member
$$- 15 x^{2} + \left(- x 7 y - y^{2}\right)$$
Let us write down the identical expression
$$- 15 x^{2} + \left(- x 7 y - y^{2}\right) = - \frac{11 y^{2}}{60} + \left(- 15 x^{2} - 7 x y - \frac{49 y^{2}}{60}\right)$$
or
$$- 15 x^{2} + \left(- x 7 y - y^{2}\right) = - \frac{11 y^{2}}{60} - \left(\sqrt{15} x + \frac{7 \sqrt{15} y}{30}\right)^{2}$$
$$- 15 x^{2} + \left(- x 7 y - y^{2}\right)$$
Let us write down the identical expression
$$- 15 x^{2} + \left(- x 7 y - y^{2}\right) = - \frac{11 y^{2}}{60} + \left(- 15 x^{2} - 7 x y - \frac{49 y^{2}}{60}\right)$$
or
$$- 15 x^{2} + \left(- x 7 y - y^{2}\right) = - \frac{11 y^{2}}{60} - \left(\sqrt{15} x + \frac{7 \sqrt{15} y}{30}\right)^{2}$$
Factorization
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/ / ____\\ / / ____\\ | y*\-7 + I*\/ 11 /| | y*\7 + I*\/ 11 /| |x - -----------------|*|x + ----------------| \ 30 / \ 30 /
$$\left(x - \frac{y \left(-7 + \sqrt{11} i\right)}{30}\right) \left(x + \frac{y \left(7 + \sqrt{11} i\right)}{30}\right)$$
(x - y*(-7 + i*sqrt(11))/30)*(x + y*(7 + i*sqrt(11))/30)
Common denominator
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2 2 - y - 15*x - 7*x*y
$$- 15 x^{2} - 7 x y - y^{2}$$
-y^2 - 15*x^2 - 7*x*y
Rational denominator
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2 2 - y - 15*x - 7*x*y
$$- 15 x^{2} - 7 x y - y^{2}$$
-y^2 - 15*x^2 - 7*x*y
Trigonometric part
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2 2 - y - 15*x - 7*x*y
$$- 15 x^{2} - 7 x y - y^{2}$$
-y^2 - 15*x^2 - 7*x*y
Assemble expression
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2 2 - y - 15*x - 7*x*y
$$- 15 x^{2} - 7 x y - y^{2}$$
-y^2 - 15*x^2 - 7*x*y
Combining rational expressions
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2 - 15*x + y*(-y - 7*x)
$$- 15 x^{2} + y \left(- 7 x - y\right)$$
-15*x^2 + y*(-y - 7*x)