Mister Exam
Factor -9*x^2-11*x*y-2*y^2 squared
The solution
You have entered
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2 2 - 9*x - 11*x*y - 2*y
$$- 2 y^{2} + \left(- 9 x^{2} - 11 x y\right)$$
-9*x^2 - 11*x*y - 2*y^2
General simplification
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2 2 - 9*x - 2*y - 11*x*y
$$- 9 x^{2} - 11 x y - 2 y^{2}$$
-9*x^2 - 2*y^2 - 11*x*y
Factorization
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/ 2*y\
(x + y)*|x + ---|
\ 9 /
$$\left(x + \frac{2 y}{9}\right) \left(x + y\right)$$
(x + y)*(x + 2*y/9)
The perfect square
Let's highlight the perfect square of the square three-member
$$- 2 y^{2} + \left(- 9 x^{2} - 11 x y\right)$$
Let us write down the identical expression
$$- 2 y^{2} + \left(- 9 x^{2} - 11 x y\right) = \frac{49 y^{2}}{36} + \left(- 9 x^{2} - 11 x y - \frac{121 y^{2}}{36}\right)$$
or
$$- 2 y^{2} + \left(- 9 x^{2} - 11 x y\right) = \frac{49 y^{2}}{36} - \left(3 x + \frac{11 y}{6}\right)^{2}$$
$$- 2 y^{2} + \left(- 9 x^{2} - 11 x y\right)$$
Let us write down the identical expression
$$- 2 y^{2} + \left(- 9 x^{2} - 11 x y\right) = \frac{49 y^{2}}{36} + \left(- 9 x^{2} - 11 x y - \frac{121 y^{2}}{36}\right)$$
or
$$- 2 y^{2} + \left(- 9 x^{2} - 11 x y\right) = \frac{49 y^{2}}{36} - \left(3 x + \frac{11 y}{6}\right)^{2}$$
Assemble expression
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2 2 - 9*x - 2*y - 11*x*y
$$- 9 x^{2} - 11 x y - 2 y^{2}$$
-9*x^2 - 2*y^2 - 11*x*y
Combinatorics
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-(x + y)*(2*y + 9*x)
$$- \left(x + y\right) \left(9 x + 2 y\right)$$
-(x + y)*(2*y + 9*x)
Trigonometric part
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2 2 - 9*x - 2*y - 11*x*y
$$- 9 x^{2} - 11 x y - 2 y^{2}$$
-9*x^2 - 2*y^2 - 11*x*y
Common denominator
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2 2 - 9*x - 2*y - 11*x*y
$$- 9 x^{2} - 11 x y - 2 y^{2}$$
-9*x^2 - 2*y^2 - 11*x*y
Combining rational expressions
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2 - 2*y + x*(-11*y - 9*x)
$$x \left(- 9 x - 11 y\right) - 2 y^{2}$$
-2*y^2 + x*(-11*y - 9*x)
Rational denominator
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2 2 - 9*x - 2*y - 11*x*y
$$- 9 x^{2} - 11 x y - 2 y^{2}$$
-9*x^2 - 2*y^2 - 11*x*y