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

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

An expression to simplify:

The solution

You have entered [src] 
 2          2
y  - y*a - a
$$- a^{2} + \left(- a y + y^{2}\right)$$ 
y^2 - y*a - a^2
General simplification [src] 
 2    2      
y  - a  - a*y
$$- a^{2} - a y + y^{2}$$ 
y^2 - a^2 - a*y
The perfect square
Let's highlight the perfect square of the square three-member
$$- a^{2} + \left(- a y + y^{2}\right)$$
Let us write down the identical expression
$$- a^{2} + \left(- a y + y^{2}\right) = \frac{5 y^{2}}{4} + \left(- a^{2} - a y - \frac{y^{2}}{4}\right)$$
or
$$- a^{2} + \left(- a y + y^{2}\right) = \frac{5 y^{2}}{4} - \left(a + \frac{y}{2}\right)^{2}$$
Factorization [src] 
/      /       ___\\ /      /      ___\\
|    y*\-1 + \/ 5 /| |    y*\1 + \/ 5 /|
|a - --------------|*|a + -------------|
\          2       / \          2      /
$$\left(a - \frac{y \left(-1 + \sqrt{5}\right)}{2}\right) \left(a + \frac{y \left(1 + \sqrt{5}\right)}{2}\right)$$ 
(a - y*(-1 + sqrt(5))/2)*(a + y*(1 + sqrt(5))/2)
Numerical answer [src] 
y^2 - a^2 - a*y
y^2 - a^2 - a*y
Powers [src] 
 2    2      
y  - a  - a*y
$$- a^{2} - a y + y^{2}$$ 
y^2 - a^2 - a*y
Assemble expression [src] 
 2    2      
y  - a  - a*y
$$- a^{2} - a y + y^{2}$$ 
y^2 - a^2 - a*y
Rational denominator [src] 
 2    2      
y  - a  - a*y
$$- a^{2} - a y + y^{2}$$ 
y^2 - a^2 - a*y
Common denominator [src] 
 2    2      
y  - a  - a*y
$$- a^{2} - a y + y^{2}$$ 
y^2 - a^2 - a*y
Combining rational expressions [src] 
   2            
- a  + y*(y - a)
$$- a^{2} + y \left(- a + y\right)$$ 
-a^2 + y*(y - a)
Trigonometric part [src] 
 2    2      
y  - a  - a*y
$$- a^{2} - a y + y^{2}$$ 
y^2 - a^2 - a*y
Combinatorics [src] 
 2    2      
y  - a  - a*y
$$- a^{2} - a y + y^{2}$$ 
y^2 - a^2 - a*y
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