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Expression simplification/ Factor perfect squares/ y^2-7*y*x-x^2

Factor y^2-7*y*x-x^2 squared

An expression to simplify:

The solution

You have entered [src] 
 2            2
y  - 7*y*x - x
$$- x^{2} + \left(- x 7 y + y^{2}\right)$$ 
y^2 - 7*y*x - x^2
General simplification [src] 
 2    2        
y  - x  - 7*x*y
$$- x^{2} - 7 x y + y^{2}$$ 
y^2 - x^2 - 7*x*y
The perfect square
Let's highlight the perfect square of the square three-member
$$- x^{2} + \left(- x 7 y + y^{2}\right)$$
Let us write down the identical expression
$$- x^{2} + \left(- x 7 y + y^{2}\right) = \frac{53 y^{2}}{4} + \left(- x^{2} - 7 x y - \frac{49 y^{2}}{4}\right)$$
or
$$- x^{2} + \left(- x 7 y + y^{2}\right) = \frac{53 y^{2}}{4} - \left(x + \frac{7 y}{2}\right)^{2}$$
Factorization [src] 
/      /       ____\\ /      /      ____\\
|    y*\-7 + \/ 53 /| |    y*\7 + \/ 53 /|
|x - ---------------|*|x + --------------|
\           2       / \          2       /
$$\left(x - \frac{y \left(-7 + \sqrt{53}\right)}{2}\right) \left(x + \frac{y \left(7 + \sqrt{53}\right)}{2}\right)$$ 
(x - y*(-7 + sqrt(53))/2)*(x + y*(7 + sqrt(53))/2)
Numerical answer [src] 
y^2 - x^2 - 7.0*x*y
y^2 - x^2 - 7.0*x*y
Assemble expression [src] 
 2    2        
y  - x  - 7*x*y
$$- x^{2} - 7 x y + y^{2}$$ 
y^2 - x^2 - 7*x*y
Combinatorics [src] 
 2    2        
y  - x  - 7*x*y
$$- x^{2} - 7 x y + y^{2}$$ 
y^2 - x^2 - 7*x*y
Combining rational expressions [src] 
   2              
- x  + y*(y - 7*x)
$$- x^{2} + y \left(- 7 x + y\right)$$ 
-x^2 + y*(y - 7*x)
Rational denominator [src] 
 2    2        
y  - x  - 7*x*y
$$- x^{2} - 7 x y + y^{2}$$ 
y^2 - x^2 - 7*x*y
Powers [src] 
 2    2        
y  - x  - 7*x*y
$$- x^{2} - 7 x y + y^{2}$$ 
y^2 - x^2 - 7*x*y
Trigonometric part [src] 
 2    2        
y  - x  - 7*x*y
$$- x^{2} - 7 x y + y^{2}$$ 
y^2 - x^2 - 7*x*y
Common denominator [src] 
 2    2        
y  - x  - 7*x*y
$$- x^{2} - 7 x y + y^{2}$$ 
y^2 - x^2 - 7*x*y
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