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Expression simplification/ Factor perfect squares/ y^2-4*y*x-3*x^2

Factor y^2-4*y*x-3*x^2 squared

An expression to simplify:

The solution

You have entered [src] 
 2              2
y  - 4*y*x - 3*x
$$- 3 x^{2} + \left(- x 4 y + y^{2}\right)$$ 
y^2 - 4*y*x - 3*x^2
General simplification [src] 
 2      2        
y  - 3*x  - 4*x*y
$$- 3 x^{2} - 4 x y + y^{2}$$ 
y^2 - 3*x^2 - 4*x*y
Factorization [src] 
/      /       ___\\ /      /      ___\\
|    y*\-2 + \/ 7 /| |    y*\2 + \/ 7 /|
|x - --------------|*|x + -------------|
\          3       / \          3      /
$$\left(x - \frac{y \left(-2 + \sqrt{7}\right)}{3}\right) \left(x + \frac{y \left(2 + \sqrt{7}\right)}{3}\right)$$ 
(x - y*(-2 + sqrt(7))/3)*(x + y*(2 + sqrt(7))/3)
The perfect square
Let's highlight the perfect square of the square three-member
$$- 3 x^{2} + \left(- x 4 y + y^{2}\right)$$
Let us write down the identical expression
$$- 3 x^{2} + \left(- x 4 y + y^{2}\right) = \frac{7 y^{2}}{3} + \left(- 3 x^{2} - 4 x y - \frac{4 y^{2}}{3}\right)$$
or
$$- 3 x^{2} + \left(- x 4 y + y^{2}\right) = \frac{7 y^{2}}{3} - \left(\sqrt{3} x + \frac{2 \sqrt{3} y}{3}\right)^{2}$$
Numerical answer [src] 
y^2 - 3.0*x^2 - 4.0*x*y
y^2 - 3.0*x^2 - 4.0*x*y
Powers [src] 
 2      2        
y  - 3*x  - 4*x*y
$$- 3 x^{2} - 4 x y + y^{2}$$ 
y^2 - 3*x^2 - 4*x*y
Assemble expression [src] 
 2      2        
y  - 3*x  - 4*x*y
$$- 3 x^{2} - 4 x y + y^{2}$$ 
y^2 - 3*x^2 - 4*x*y
Rational denominator [src] 
 2      2        
y  - 3*x  - 4*x*y
$$- 3 x^{2} - 4 x y + y^{2}$$ 
y^2 - 3*x^2 - 4*x*y
Common denominator [src] 
 2      2        
y  - 3*x  - 4*x*y
$$- 3 x^{2} - 4 x y + y^{2}$$ 
y^2 - 3*x^2 - 4*x*y
Trigonometric part [src] 
 2      2        
y  - 3*x  - 4*x*y
$$- 3 x^{2} - 4 x y + y^{2}$$ 
y^2 - 3*x^2 - 4*x*y
Combinatorics [src] 
 2      2        
y  - 3*x  - 4*x*y
$$- 3 x^{2} - 4 x y + y^{2}$$ 
y^2 - 3*x^2 - 4*x*y
Combining rational expressions [src] 
     2              
- 3*x  + y*(y - 4*x)
$$- 3 x^{2} + y \left(- 4 x + y\right)$$ 
-3*x^2 + y*(y - 4*x)
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