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Expression simplification/ Factor perfect squares/ x^2-13*x*y+3*y^2

Factor x^2-13*x*y+3*y^2 squared

An expression to simplify:

The solution

You have entered [src] 
 2               2
x  - 13*x*y + 3*y
$$3 y^{2} + \left(x^{2} - 13 x y\right)$$ 
x^2 - 13*x*y + 3*y^2
The perfect square
Let's highlight the perfect square of the square three-member
$$3 y^{2} + \left(x^{2} - 13 x y\right)$$
Let us write down the identical expression
$$3 y^{2} + \left(x^{2} - 13 x y\right) = - \frac{157 y^{2}}{4} + \left(x^{2} - 13 x y + \frac{169 y^{2}}{4}\right)$$
or
$$3 y^{2} + \left(x^{2} - 13 x y\right) = - \frac{157 y^{2}}{4} + \left(x - \frac{13 y}{2}\right)^{2}$$
in the view of the product
$$\left(- \sqrt{\frac{157}{4}} y + \left(x - \frac{13 y}{2}\right)\right) \left(\sqrt{\frac{157}{4}} y + \left(x - \frac{13 y}{2}\right)\right)$$
$$\left(- \frac{\sqrt{157}}{2} y + \left(x - \frac{13 y}{2}\right)\right) \left(\frac{\sqrt{157}}{2} y + \left(x - \frac{13 y}{2}\right)\right)$$
$$\left(x + y \left(- \frac{13}{2} - \frac{\sqrt{157}}{2}\right)\right) \left(x + y \left(- \frac{13}{2} + \frac{\sqrt{157}}{2}\right)\right)$$
$$\left(x + y \left(- \frac{13}{2} - \frac{\sqrt{157}}{2}\right)\right) \left(x + y \left(- \frac{13}{2} + \frac{\sqrt{157}}{2}\right)\right)$$
General simplification [src] 
 2      2         
x  + 3*y  - 13*x*y
$$x^{2} - 13 x y + 3 y^{2}$$ 
x^2 + 3*y^2 - 13*x*y
Factorization [src] 
/      /       _____\\ /      /       _____\\
|    y*\13 - \/ 157 /| |    y*\13 + \/ 157 /|
|x - ----------------|*|x - ----------------|
\           2        / \           2        /
$$\left(x - \frac{y \left(13 - \sqrt{157}\right)}{2}\right) \left(x - \frac{y \left(\sqrt{157} + 13\right)}{2}\right)$$ 
(x - y*(13 - sqrt(157))/2)*(x - y*(13 + sqrt(157))/2)
Assemble expression [src] 
 2      2         
x  + 3*y  - 13*x*y
$$x^{2} - 13 x y + 3 y^{2}$$ 
x^2 + 3*y^2 - 13*x*y
Trigonometric part [src] 
 2      2         
x  + 3*y  - 13*x*y
$$x^{2} - 13 x y + 3 y^{2}$$ 
x^2 + 3*y^2 - 13*x*y
Common denominator [src] 
 2      2         
x  + 3*y  - 13*x*y
$$x^{2} - 13 x y + 3 y^{2}$$ 
x^2 + 3*y^2 - 13*x*y
Combinatorics [src] 
 2      2         
x  + 3*y  - 13*x*y
$$x^{2} - 13 x y + 3 y^{2}$$ 
x^2 + 3*y^2 - 13*x*y
Numerical answer [src] 
x^2 + 3.0*y^2 - 13.0*x*y
x^2 + 3.0*y^2 - 13.0*x*y
Powers [src] 
 2      2         
x  + 3*y  - 13*x*y
$$x^{2} - 13 x y + 3 y^{2}$$ 
x^2 + 3*y^2 - 13*x*y
Rational denominator [src] 
 2      2         
x  + 3*y  - 13*x*y
$$x^{2} - 13 x y + 3 y^{2}$$ 
x^2 + 3*y^2 - 13*x*y
Combining rational expressions [src] 
   2               
3*y  + x*(x - 13*y)
$$x \left(x - 13 y\right) + 3 y^{2}$$ 
3*y^2 + x*(x - 13*y)
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