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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
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
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
$$8 x^{2} + \left(x 8 y - y^{2}\right) = - 3 y^{2} + \left(8 x^{2} + 8 x y + 2 y^{2}\right)$$
or
$$8 x^{2} + \left(x 8 y - y^{2}\right) = - 3 y^{2} + \left(2 \sqrt{2} x + \sqrt{2} y\right)^{2}$$
in the view of the product
$$\left(- \sqrt{3} y + \left(2 \sqrt{2} x + \sqrt{2} y\right)\right) \left(\sqrt{3} y + \left(2 \sqrt{2} x + \sqrt{2} y\right)\right)$$
$$\left(- \sqrt{3} y + \left(2 \sqrt{2} x + \sqrt{2} y\right)\right) \left(\sqrt{3} y + \left(2 \sqrt{2} x + \sqrt{2} y\right)\right)$$
$$\left(2 \sqrt{2} x + y \left(\sqrt{2} + \sqrt{3}\right)\right) \left(2 \sqrt{2} x + y \left(- \sqrt{3} + \sqrt{2}\right)\right)$$
$$\left(2 \sqrt{2} x + y \left(\sqrt{2} + \sqrt{3}\right)\right) \left(2 \sqrt{2} x + y \left(- \sqrt{3} + \sqrt{2}\right)\right)$$
Factorization [src] 
/      /       ___\\ /      /      ___\\
|    y*\-2 + \/ 6 /| |    y*\2 + \/ 6 /|
|x - --------------|*|x + -------------|
\          4       / \          4      /
$$\left(x - \frac{y \left(-2 + \sqrt{6}\right)}{4}\right) \left(x + \frac{y \left(2 + \sqrt{6}\right)}{4}\right)$$ 
(x - y*(-2 + sqrt(6))/4)*(x + y*(2 + sqrt(6))/4)
Numerical answer [src] 
-y^2 + 8.0*x^2 + 8.0*x*y
-y^2 + 8.0*x^2 + 8.0*x*y
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
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
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
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
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)
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
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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