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Expression simplification/ Factor perfect squares/ -y^2-8*y*x-8*x^2

Factor -y^2-8*y*x-8*x^2 squared

An expression to simplify:

The solution

You have entered [src] 
   2              2
- y  - 8*y*x - 8*x
$$- 8 x^{2} + \left(- x 8 y - y^{2}\right)$$ 
-y^2 - 8*y*x - 8*x^2
The perfect square
Let's highlight the perfect square of the square three-member
$$- 8 x^{2} + \left(- x 8 y - y^{2}\right)$$
Let us write down the identical expression
$$- 8 x^{2} + \left(- x 8 y - y^{2}\right) = y^{2} + \left(- 8 x^{2} - 8 x y - 2 y^{2}\right)$$
or
$$- 8 x^{2} + \left(- x 8 y - y^{2}\right) = y^{2} - \left(2 \sqrt{2} x + \sqrt{2} y\right)^{2}$$
General simplification [src] 
   2      2        
- y  - 8*x  - 8*x*y
$$- 8 x^{2} - 8 x y - y^{2}$$ 
-y^2 - 8*x^2 - 8*x*y
Factorization [src] 
/      /       ___\\ /      /      ___\\
|    y*\-2 + \/ 2 /| |    y*\2 + \/ 2 /|
|x - --------------|*|x + -------------|
\          4       / \          4      /
$$\left(x - \frac{y \left(-2 + \sqrt{2}\right)}{4}\right) \left(x + \frac{y \left(\sqrt{2} + 2\right)}{4}\right)$$ 
(x - y*(-2 + sqrt(2))/4)*(x + y*(2 + sqrt(2))/4)
Numerical answer [src] 
-y^2 - 8.0*x^2 - 8.0*x*y
-y^2 - 8.0*x^2 - 8.0*x*y
Powers [src] 
   2      2        
- y  - 8*x  - 8*x*y
$$- 8 x^{2} - 8 x y - y^{2}$$ 
-y^2 - 8*x^2 - 8*x*y
Combining rational expressions [src] 
     2               
- 8*x  + y*(-y - 8*x)
$$- 8 x^{2} + y \left(- 8 x - y\right)$$ 
-8*x^2 + y*(-y - 8*x)
Combinatorics [src] 
   2      2        
- y  - 8*x  - 8*x*y
$$- 8 x^{2} - 8 x y - y^{2}$$ 
-y^2 - 8*x^2 - 8*x*y
Rational denominator [src] 
   2      2        
- y  - 8*x  - 8*x*y
$$- 8 x^{2} - 8 x y - y^{2}$$ 
-y^2 - 8*x^2 - 8*x*y
Trigonometric part [src] 
   2      2        
- y  - 8*x  - 8*x*y
$$- 8 x^{2} - 8 x y - y^{2}$$ 
-y^2 - 8*x^2 - 8*x*y
Common denominator [src] 
   2      2        
- y  - 8*x  - 8*x*y
$$- 8 x^{2} - 8 x y - y^{2}$$ 
-y^2 - 8*x^2 - 8*x*y
Assemble expression [src] 
   2      2        
- y  - 8*x  - 8*x*y
$$- 8 x^{2} - 8 x y - y^{2}$$ 
-y^2 - 8*x^2 - 8*x*y
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