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Expression simplification/ Factor perfect squares/ y^2-9*y*t-5*t^2

Factor y^2-9*y*t-5*t^2 squared

An expression to simplify:

The solution

You have entered [src] 
 2              2
y  - 9*y*t - 5*t
$$- 5 t^{2} + \left(- t 9 y + y^{2}\right)$$ 
y^2 - 9*y*t - 5*t^2
General simplification [src] 
 2      2        
y  - 5*t  - 9*t*y
$$- 5 t^{2} - 9 t y + y^{2}$$ 
y^2 - 5*t^2 - 9*t*y
The perfect square
Let's highlight the perfect square of the square three-member
$$- 5 t^{2} + \left(- t 9 y + y^{2}\right)$$
Let us write down the identical expression
$$- 5 t^{2} + \left(- t 9 y + y^{2}\right) = \frac{101 y^{2}}{20} + \left(- 5 t^{2} - 9 t y - \frac{81 y^{2}}{20}\right)$$
or
$$- 5 t^{2} + \left(- t 9 y + y^{2}\right) = \frac{101 y^{2}}{20} - \left(\sqrt{5} t + \frac{9 \sqrt{5} y}{10}\right)^{2}$$
Factorization [src] 
/      /       _____\\ /      /      _____\\
|    y*\-9 + \/ 101 /| |    y*\9 + \/ 101 /|
|t - ----------------|*|t + ---------------|
\           10       / \           10      /
$$\left(t - \frac{y \left(-9 + \sqrt{101}\right)}{10}\right) \left(t + \frac{y \left(9 + \sqrt{101}\right)}{10}\right)$$ 
(t - y*(-9 + sqrt(101))/10)*(t + y*(9 + sqrt(101))/10)
Combining rational expressions [src] 
     2              
- 5*t  + y*(y - 9*t)
$$- 5 t^{2} + y \left(- 9 t + y\right)$$ 
-5*t^2 + y*(y - 9*t)
Trigonometric part [src] 
 2      2        
y  - 5*t  - 9*t*y
$$- 5 t^{2} - 9 t y + y^{2}$$ 
y^2 - 5*t^2 - 9*t*y
Rational denominator [src] 
 2      2        
y  - 5*t  - 9*t*y
$$- 5 t^{2} - 9 t y + y^{2}$$ 
y^2 - 5*t^2 - 9*t*y
Powers [src] 
 2      2        
y  - 5*t  - 9*t*y
$$- 5 t^{2} - 9 t y + y^{2}$$ 
y^2 - 5*t^2 - 9*t*y
Combinatorics [src] 
 2      2        
y  - 5*t  - 9*t*y
$$- 5 t^{2} - 9 t y + y^{2}$$ 
y^2 - 5*t^2 - 9*t*y
Assemble expression [src] 
 2      2        
y  - 5*t  - 9*t*y
$$- 5 t^{2} - 9 t y + y^{2}$$ 
y^2 - 5*t^2 - 9*t*y
Common denominator [src] 
 2      2        
y  - 5*t  - 9*t*y
$$- 5 t^{2} - 9 t y + y^{2}$$ 
y^2 - 5*t^2 - 9*t*y
Numerical answer [src] 
y^2 - 5.0*t^2 - 9.0*t*y
y^2 - 5.0*t^2 - 9.0*t*y
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