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

Factor y^2-4*y*t+3*t^2 squared

An expression to simplify:

The solution

You have entered [src] 
 2              2
y  - 4*y*t + 3*t
$$3 t^{2} + \left(- t 4 y + y^{2}\right)$$ 
y^2 - 4*y*t + 3*t^2
The perfect square
Let's highlight the perfect square of the square three-member
$$3 t^{2} + \left(- t 4 y + y^{2}\right)$$
Let us write down the identical expression
$$3 t^{2} + \left(- t 4 y + y^{2}\right) = - \frac{y^{2}}{3} + \left(3 t^{2} - 4 t y + \frac{4 y^{2}}{3}\right)$$
or
$$3 t^{2} + \left(- t 4 y + y^{2}\right) = - \frac{y^{2}}{3} + \left(\sqrt{3} t - \frac{2 \sqrt{3} y}{3}\right)^{2}$$
in the view of the product
$$\left(- \frac{y}{\sqrt{3}} + \left(\sqrt{3} t + - \frac{2 \sqrt{3}}{3} y\right)\right) \left(\frac{y}{\sqrt{3}} + \left(\sqrt{3} t + - \frac{2 \sqrt{3}}{3} y\right)\right)$$
$$\left(- \frac{\sqrt{3}}{3} y + \left(\sqrt{3} t + - \frac{2 \sqrt{3}}{3} y\right)\right) \left(\frac{\sqrt{3}}{3} y + \left(\sqrt{3} t + - \frac{2 \sqrt{3}}{3} y\right)\right)$$
$$\left(\sqrt{3} t + y \left(- \frac{2 \sqrt{3}}{3} - \frac{\sqrt{3}}{3}\right)\right) \left(\sqrt{3} t + y \left(- \frac{2 \sqrt{3}}{3} + \frac{\sqrt{3}}{3}\right)\right)$$
$$\left(\sqrt{3} t - \sqrt{3} y\right) \left(\sqrt{3} t - \frac{\sqrt{3} y}{3}\right)$$
General simplification [src] 
 2      2        
y  + 3*t  - 4*t*y
$$3 t^{2} - 4 t y + y^{2}$$ 
y^2 + 3*t^2 - 4*t*y
Factorization [src] 
/    y\        
|t - -|*(t - y)
\    3/
$$\left(t - y\right) \left(t - \frac{y}{3}\right)$$ 
(t - y/3)*(t - y)
Numerical answer [src] 
y^2 + 3.0*t^2 - 4.0*t*y
y^2 + 3.0*t^2 - 4.0*t*y
Common denominator [src] 
 2      2        
y  + 3*t  - 4*t*y
$$3 t^{2} - 4 t y + y^{2}$$ 
y^2 + 3*t^2 - 4*t*y
Trigonometric part [src] 
 2      2        
y  + 3*t  - 4*t*y
$$3 t^{2} - 4 t y + y^{2}$$ 
y^2 + 3*t^2 - 4*t*y
Combining rational expressions [src] 
   2              
3*t  + y*(y - 4*t)
$$3 t^{2} + y \left(- 4 t + y\right)$$ 
3*t^2 + y*(y - 4*t)
Assemble expression [src] 
 2      2        
y  + 3*t  - 4*t*y
$$3 t^{2} - 4 t y + y^{2}$$ 
y^2 + 3*t^2 - 4*t*y
Combinatorics [src] 
(y - t)*(y - 3*t)
$$\left(- 3 t + y\right) \left(- t + y\right)$$ 
(y - t)*(y - 3*t)
Rational denominator [src] 
 2      2        
y  + 3*t  - 4*t*y
$$3 t^{2} - 4 t y + y^{2}$$ 
y^2 + 3*t^2 - 4*t*y
Powers [src] 
 2      2        
y  + 3*t  - 4*t*y
$$3 t^{2} - 4 t y + y^{2}$$ 
y^2 + 3*t^2 - 4*t*y
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