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Expression simplification/ Factor perfect squares/ y^2-y*x-5*x^2

Factor y^2-y*x-5*x^2 squared

An expression to simplify:

The solution

You have entered [src] 
 2            2
y  - y*x - 5*x
$$- 5 x^{2} + \left(- x y + y^{2}\right)$$ 
y^2 - y*x - 5*x^2
General simplification [src] 
 2      2      
y  - 5*x  - x*y
$$- 5 x^{2} - x y + y^{2}$$ 
y^2 - 5*x^2 - x*y
The perfect square
Let's highlight the perfect square of the square three-member
$$- 5 x^{2} + \left(- x y + y^{2}\right)$$
Let us write down the identical expression
$$- 5 x^{2} + \left(- x y + y^{2}\right) = \frac{21 y^{2}}{20} + \left(- 5 x^{2} - x y - \frac{y^{2}}{20}\right)$$
or
$$- 5 x^{2} + \left(- x y + y^{2}\right) = \frac{21 y^{2}}{20} - \left(\sqrt{5} x + \frac{\sqrt{5} y}{10}\right)^{2}$$
Factorization [src] 
/      /       ____\\ /      /      ____\\
|    y*\-1 + \/ 21 /| |    y*\1 + \/ 21 /|
|x - ---------------|*|x + --------------|
\           10      / \          10      /
$$\left(x - \frac{y \left(-1 + \sqrt{21}\right)}{10}\right) \left(x + \frac{y \left(1 + \sqrt{21}\right)}{10}\right)$$ 
(x - y*(-1 + sqrt(21))/10)*(x + y*(1 + sqrt(21))/10)
Numerical answer [src] 
y^2 - 5.0*x^2 - x*y
y^2 - 5.0*x^2 - x*y
Rational denominator [src] 
 2      2      
y  - 5*x  - x*y
$$- 5 x^{2} - x y + y^{2}$$ 
y^2 - 5*x^2 - x*y
Assemble expression [src] 
 2      2      
y  - 5*x  - x*y
$$- 5 x^{2} - x y + y^{2}$$ 
y^2 - 5*x^2 - x*y
Common denominator [src] 
 2      2      
y  - 5*x  - x*y
$$- 5 x^{2} - x y + y^{2}$$ 
y^2 - 5*x^2 - x*y
Trigonometric part [src] 
 2      2      
y  - 5*x  - x*y
$$- 5 x^{2} - x y + y^{2}$$ 
y^2 - 5*x^2 - x*y
Combining rational expressions [src] 
     2            
- 5*x  + y*(y - x)
$$- 5 x^{2} + y \left(- x + y\right)$$ 
-5*x^2 + y*(y - x)
Combinatorics [src] 
 2      2      
y  - 5*x  - x*y
$$- 5 x^{2} - x y + y^{2}$$ 
y^2 - 5*x^2 - x*y
Powers [src] 
 2      2      
y  - 5*x  - x*y
$$- 5 x^{2} - x y + y^{2}$$ 
y^2 - 5*x^2 - x*y
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