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Expression simplification/ Factor perfect squares/ y^2-y*t-6*t^2

Factor y^2-y*t-6*t^2 squared

An expression to simplify:

The solution

You have entered [src] 
 2            2
y  - y*t - 6*t
$$- 6 t^{2} + \left(- t y + y^{2}\right)$$ 
y^2 - y*t - 6*t^2
The perfect square
Let's highlight the perfect square of the square three-member
$$- 6 t^{2} + \left(- t y + y^{2}\right)$$
Let us write down the identical expression
$$- 6 t^{2} + \left(- t y + y^{2}\right) = \frac{25 y^{2}}{24} + \left(- 6 t^{2} - t y - \frac{y^{2}}{24}\right)$$
or
$$- 6 t^{2} + \left(- t y + y^{2}\right) = \frac{25 y^{2}}{24} - \left(\sqrt{6} t + \frac{\sqrt{6} y}{12}\right)^{2}$$
Factorization [src] 
/    y\ /    y\
|t + -|*|t - -|
\    2/ \    3/
$$\left(t - \frac{y}{3}\right) \left(t + \frac{y}{2}\right)$$ 
(t + y/2)*(t - y/3)
General simplification [src] 
 2      2      
y  - 6*t  - t*y
$$- 6 t^{2} - t y + y^{2}$$ 
y^2 - 6*t^2 - t*y
Numerical answer [src] 
y^2 - 6.0*t^2 - t*y
y^2 - 6.0*t^2 - t*y
Common denominator [src] 
 2      2      
y  - 6*t  - t*y
$$- 6 t^{2} - t y + y^{2}$$ 
y^2 - 6*t^2 - t*y
Trigonometric part [src] 
 2      2      
y  - 6*t  - t*y
$$- 6 t^{2} - t y + y^{2}$$ 
y^2 - 6*t^2 - t*y
Assemble expression [src] 
 2      2      
y  - 6*t  - t*y
$$- 6 t^{2} - t y + y^{2}$$ 
y^2 - 6*t^2 - t*y
Rational denominator [src] 
 2      2      
y  - 6*t  - t*y
$$- 6 t^{2} - t y + y^{2}$$ 
y^2 - 6*t^2 - t*y
Powers [src] 
 2      2      
y  - 6*t  - t*y
$$- 6 t^{2} - t y + y^{2}$$ 
y^2 - 6*t^2 - t*y
Combinatorics [src] 
(y - 3*t)*(y + 2*t)
$$\left(- 3 t + y\right) \left(2 t + y\right)$$ 
(y - 3*t)*(y + 2*t)
Combining rational expressions [src] 
     2            
- 6*t  + y*(y - t)
$$- 6 t^{2} + y \left(- t + y\right)$$ 
-6*t^2 + y*(y - t)
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