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Expression simplification/ Factor perfect squares/ -y^2-5*y*a+a^2

Factor -y^2-5*y*a+a^2 squared

An expression to simplify:

The solution

You have entered [src] 
   2            2
- y  - 5*y*a + a
$$a^{2} + \left(- a 5 y - y^{2}\right)$$ 
-y^2 - 5*y*a + a^2
The perfect square
Let's highlight the perfect square of the square three-member
$$a^{2} + \left(- a 5 y - y^{2}\right)$$
Let us write down the identical expression
$$a^{2} + \left(- a 5 y - y^{2}\right) = - \frac{29 y^{2}}{4} + \left(a^{2} - 5 a y + \frac{25 y^{2}}{4}\right)$$
or
$$a^{2} + \left(- a 5 y - y^{2}\right) = - \frac{29 y^{2}}{4} + \left(a - \frac{5 y}{2}\right)^{2}$$
in the view of the product
$$\left(- \sqrt{\frac{29}{4}} y + \left(a - \frac{5 y}{2}\right)\right) \left(\sqrt{\frac{29}{4}} y + \left(a - \frac{5 y}{2}\right)\right)$$
$$\left(- \frac{\sqrt{29}}{2} y + \left(a - \frac{5 y}{2}\right)\right) \left(\frac{\sqrt{29}}{2} y + \left(a - \frac{5 y}{2}\right)\right)$$
$$\left(a + y \left(- \frac{5}{2} + \frac{\sqrt{29}}{2}\right)\right) \left(a + y \left(- \frac{\sqrt{29}}{2} - \frac{5}{2}\right)\right)$$
$$\left(a + y \left(- \frac{5}{2} + \frac{\sqrt{29}}{2}\right)\right) \left(a + y \left(- \frac{\sqrt{29}}{2} - \frac{5}{2}\right)\right)$$
Factorization [src] 
/      /      ____\\ /      /      ____\\
|    y*\5 - \/ 29 /| |    y*\5 + \/ 29 /|
|a - --------------|*|a - --------------|
\          2       / \          2       /
$$\left(a - \frac{y \left(5 - \sqrt{29}\right)}{2}\right) \left(a - \frac{y \left(5 + \sqrt{29}\right)}{2}\right)$$ 
(a - y*(5 - sqrt(29))/2)*(a - y*(5 + sqrt(29))/2)
General simplification [src] 
 2    2        
a  - y  - 5*a*y
$$a^{2} - 5 a y - y^{2}$$ 
a^2 - y^2 - 5*a*y
Numerical answer [src] 
a^2 - y^2 - 5.0*a*y
a^2 - y^2 - 5.0*a*y
Trigonometric part [src] 
 2    2        
a  - y  - 5*a*y
$$a^{2} - 5 a y - y^{2}$$ 
a^2 - y^2 - 5*a*y
Assemble expression [src] 
 2    2        
a  - y  - 5*a*y
$$a^{2} - 5 a y - y^{2}$$ 
a^2 - y^2 - 5*a*y
Combining rational expressions [src] 
 2               
a  + y*(-y - 5*a)
$$a^{2} + y \left(- 5 a - y\right)$$ 
a^2 + y*(-y - 5*a)
Common denominator [src] 
 2    2        
a  - y  - 5*a*y
$$a^{2} - 5 a y - y^{2}$$ 
a^2 - y^2 - 5*a*y
Powers [src] 
 2    2        
a  - y  - 5*a*y
$$a^{2} - 5 a y - y^{2}$$ 
a^2 - y^2 - 5*a*y
Combinatorics [src] 
 2    2        
a  - y  - 5*a*y
$$a^{2} - 5 a y - y^{2}$$ 
a^2 - y^2 - 5*a*y
Rational denominator [src] 
 2    2        
a  - y  - 5*a*y
$$a^{2} - 5 a y - y^{2}$$ 
a^2 - y^2 - 5*a*y
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