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Expression simplification/ Factor perfect squares/ -y^2-y*x+15*x^2

Factor -y^2-y*x+15*x^2 squared

An expression to simplify:

The solution

You have entered [src] 
   2             2
- y  - y*x + 15*x
$$15 x^{2} + \left(- x y - y^{2}\right)$$ 
-y^2 - y*x + 15*x^2
The perfect square
Let's highlight the perfect square of the square three-member
$$15 x^{2} + \left(- x y - y^{2}\right)$$
Let us write down the identical expression
$$15 x^{2} + \left(- x y - y^{2}\right) = - \frac{61 y^{2}}{60} + \left(15 x^{2} - x y + \frac{y^{2}}{60}\right)$$
or
$$15 x^{2} + \left(- x y - y^{2}\right) = - \frac{61 y^{2}}{60} + \left(\sqrt{15} x - \frac{\sqrt{15} y}{30}\right)^{2}$$
in the view of the product
$$\left(- \sqrt{\frac{61}{60}} y + \left(\sqrt{15} x + - \frac{\sqrt{15}}{30} y\right)\right) \left(\sqrt{\frac{61}{60}} y + \left(\sqrt{15} x + - \frac{\sqrt{15}}{30} y\right)\right)$$
$$\left(- \frac{\sqrt{915}}{30} y + \left(\sqrt{15} x + - \frac{\sqrt{15}}{30} y\right)\right) \left(\frac{\sqrt{915}}{30} y + \left(\sqrt{15} x + - \frac{\sqrt{15}}{30} y\right)\right)$$
$$\left(\sqrt{15} x + y \left(- \frac{\sqrt{15}}{30} + \frac{\sqrt{915}}{30}\right)\right) \left(\sqrt{15} x + y \left(- \frac{\sqrt{915}}{30} - \frac{\sqrt{15}}{30}\right)\right)$$
$$\left(\sqrt{15} x + y \left(- \frac{\sqrt{15}}{30} + \frac{\sqrt{915}}{30}\right)\right) \left(\sqrt{15} x + y \left(- \frac{\sqrt{915}}{30} - \frac{\sqrt{15}}{30}\right)\right)$$
General simplification [src] 
   2       2      
- y  + 15*x  - x*y
$$15 x^{2} - x y - y^{2}$$ 
-y^2 + 15*x^2 - x*y
Factorization [src] 
/      /      ____\\ /      /      ____\\
|    y*\1 - \/ 61 /| |    y*\1 + \/ 61 /|
|x - --------------|*|x - --------------|
\          30      / \          30      /
$$\left(x - \frac{y \left(1 - \sqrt{61}\right)}{30}\right) \left(x - \frac{y \left(1 + \sqrt{61}\right)}{30}\right)$$ 
(x - y*(1 - sqrt(61))/30)*(x - y*(1 + sqrt(61))/30)
Numerical answer [src] 
-y^2 + 15.0*x^2 - x*y
-y^2 + 15.0*x^2 - x*y
Combining rational expressions [src] 
    2             
15*x  + y*(-x - y)
$$15 x^{2} + y \left(- x - y\right)$$ 
15*x^2 + y*(-x - y)
Powers [src] 
   2       2      
- y  + 15*x  - x*y
$$15 x^{2} - x y - y^{2}$$ 
-y^2 + 15*x^2 - x*y
Assemble expression [src] 
   2       2      
- y  + 15*x  - x*y
$$15 x^{2} - x y - y^{2}$$ 
-y^2 + 15*x^2 - x*y
Combinatorics [src] 
   2       2      
- y  + 15*x  - x*y
$$15 x^{2} - x y - y^{2}$$ 
-y^2 + 15*x^2 - x*y
Common denominator [src] 
   2       2      
- y  + 15*x  - x*y
$$15 x^{2} - x y - y^{2}$$ 
-y^2 + 15*x^2 - x*y
Trigonometric part [src] 
   2       2      
- y  + 15*x  - x*y
$$15 x^{2} - x y - y^{2}$$ 
-y^2 + 15*x^2 - x*y
Rational denominator [src] 
   2       2      
- y  + 15*x  - x*y
$$15 x^{2} - x y - y^{2}$$ 
-y^2 + 15*x^2 - x*y
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