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

Factor y^2-y*b-9*b^2 squared

An expression to simplify:

The solution

You have entered [src] 
 2            2
y  - y*b - 9*b
$$- 9 b^{2} + \left(- b y + y^{2}\right)$$ 
y^2 - y*b - 9*b^2
General simplification [src] 
 2      2      
y  - 9*b  - b*y
$$- 9 b^{2} - b y + y^{2}$$ 
y^2 - 9*b^2 - b*y
Factorization [src] 
/      /       ____\\ /      /      ____\\
|    y*\-1 + \/ 37 /| |    y*\1 + \/ 37 /|
|b - ---------------|*|b + --------------|
\           18      / \          18      /
$$\left(b - \frac{y \left(-1 + \sqrt{37}\right)}{18}\right) \left(b + \frac{y \left(1 + \sqrt{37}\right)}{18}\right)$$ 
(b - y*(-1 + sqrt(37))/18)*(b + y*(1 + sqrt(37))/18)
The perfect square
Let's highlight the perfect square of the square three-member
$$- 9 b^{2} + \left(- b y + y^{2}\right)$$
Let us write down the identical expression
$$- 9 b^{2} + \left(- b y + y^{2}\right) = \frac{37 y^{2}}{36} + \left(- 9 b^{2} - b y - \frac{y^{2}}{36}\right)$$
or
$$- 9 b^{2} + \left(- b y + y^{2}\right) = \frac{37 y^{2}}{36} - \left(3 b + \frac{y}{6}\right)^{2}$$
Numerical answer [src] 
y^2 - 9.0*b^2 - b*y
y^2 - 9.0*b^2 - b*y
Combining rational expressions [src] 
     2            
- 9*b  + y*(y - b)
$$- 9 b^{2} + y \left(- b + y\right)$$ 
-9*b^2 + y*(y - b)
Assemble expression [src] 
 2      2      
y  - 9*b  - b*y
$$- 9 b^{2} - b y + y^{2}$$ 
y^2 - 9*b^2 - b*y
Powers [src] 
 2      2      
y  - 9*b  - b*y
$$- 9 b^{2} - b y + y^{2}$$ 
y^2 - 9*b^2 - b*y
Rational denominator [src] 
 2      2      
y  - 9*b  - b*y
$$- 9 b^{2} - b y + y^{2}$$ 
y^2 - 9*b^2 - b*y
Trigonometric part [src] 
 2      2      
y  - 9*b  - b*y
$$- 9 b^{2} - b y + y^{2}$$ 
y^2 - 9*b^2 - b*y
Common denominator [src] 
 2      2      
y  - 9*b  - b*y
$$- 9 b^{2} - b y + y^{2}$$ 
y^2 - 9*b^2 - b*y
Combinatorics [src] 
 2      2      
y  - 9*b  - b*y
$$- 9 b^{2} - b y + y^{2}$$ 
y^2 - 9*b^2 - b*y
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