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Expression simplification/ Factor perfect squares/ y^2-y*b+10*b^2

Factor y^2-y*b+10*b^2 squared

An expression to simplify:

The solution

You have entered [src] 
 2             2
y  - y*b + 10*b
$$10 b^{2} + \left(- b y + y^{2}\right)$$ 
y^2 - y*b + 10*b^2
General simplification [src] 
 2       2      
y  + 10*b  - b*y
$$10 b^{2} - b y + y^{2}$$ 
y^2 + 10*b^2 - b*y
The perfect square
Let's highlight the perfect square of the square three-member
$$10 b^{2} + \left(- b y + y^{2}\right)$$
Let us write down the identical expression
$$10 b^{2} + \left(- b y + y^{2}\right) = \frac{39 y^{2}}{40} + \left(10 b^{2} - b y + \frac{y^{2}}{40}\right)$$
or
$$10 b^{2} + \left(- b y + y^{2}\right) = \frac{39 y^{2}}{40} + \left(\sqrt{10} b - \frac{\sqrt{10} y}{20}\right)^{2}$$
Factorization [src] 
/      /        ____\\ /      /        ____\\
|    y*\1 - I*\/ 39 /| |    y*\1 + I*\/ 39 /|
|b - ----------------|*|b - ----------------|
\           20       / \           20       /
$$\left(b - \frac{y \left(1 - \sqrt{39} i\right)}{20}\right) \left(b - \frac{y \left(1 + \sqrt{39} i\right)}{20}\right)$$ 
(b - y*(1 - i*sqrt(39))/20)*(b - y*(1 + i*sqrt(39))/20)
Combinatorics [src] 
 2       2      
y  + 10*b  - b*y
$$10 b^{2} - b y + y^{2}$$ 
y^2 + 10*b^2 - b*y
Rational denominator [src] 
 2       2      
y  + 10*b  - b*y
$$10 b^{2} - b y + y^{2}$$ 
y^2 + 10*b^2 - b*y
Trigonometric part [src] 
 2       2      
y  + 10*b  - b*y
$$10 b^{2} - b y + y^{2}$$ 
y^2 + 10*b^2 - b*y
Assemble expression [src] 
 2       2      
y  + 10*b  - b*y
$$10 b^{2} - b y + y^{2}$$ 
y^2 + 10*b^2 - b*y
Numerical answer [src] 
y^2 + 10.0*b^2 - b*y
y^2 + 10.0*b^2 - b*y
Powers [src] 
 2       2      
y  + 10*b  - b*y
$$10 b^{2} - b y + y^{2}$$ 
y^2 + 10*b^2 - b*y
Common denominator [src] 
 2       2      
y  + 10*b  - b*y
$$10 b^{2} - b y + y^{2}$$ 
y^2 + 10*b^2 - b*y
Combining rational expressions [src] 
    2            
10*b  + y*(y - b)
$$10 b^{2} + y \left(- b + y\right)$$ 
10*b^2 + y*(y - b)
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