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Expression simplification/ Factor perfect squares/ y^2+7*y*b-b^2

Factor y^2+7*y*b-b^2 squared

An expression to simplify:

The solution

You have entered [src] 
 2            2
y  + 7*y*b - b
$$- b^{2} + \left(b 7 y + y^{2}\right)$$ 
y^2 + (7*y)*b - b^2
General simplification [src] 
 2    2        
y  - b  + 7*b*y
$$- b^{2} + 7 b y + y^{2}$$ 
y^2 - b^2 + 7*b*y
Factorization [src] 
/      /      ____\\ /      /      ____\\
|    y*\7 - \/ 53 /| |    y*\7 + \/ 53 /|
|b - --------------|*|b - --------------|
\          2       / \          2       /
$$\left(b - \frac{y \left(7 - \sqrt{53}\right)}{2}\right) \left(b - \frac{y \left(7 + \sqrt{53}\right)}{2}\right)$$ 
(b - y*(7 - sqrt(53))/2)*(b - y*(7 + sqrt(53))/2)
The perfect square
Let's highlight the perfect square of the square three-member
$$- b^{2} + \left(b 7 y + y^{2}\right)$$
Let us write down the identical expression
$$- b^{2} + \left(b 7 y + y^{2}\right) = \frac{53 y^{2}}{4} + \left(- b^{2} + 7 b y - \frac{49 y^{2}}{4}\right)$$
or
$$- b^{2} + \left(b 7 y + y^{2}\right) = \frac{53 y^{2}}{4} - \left(b - \frac{7 y}{2}\right)^{2}$$
Common denominator [src] 
 2    2        
y  - b  + 7*b*y
$$- b^{2} + 7 b y + y^{2}$$ 
y^2 - b^2 + 7*b*y
Powers [src] 
 2    2        
y  - b  + 7*b*y
$$- b^{2} + 7 b y + y^{2}$$ 
y^2 - b^2 + 7*b*y
Combinatorics [src] 
 2    2        
y  - b  + 7*b*y
$$- b^{2} + 7 b y + y^{2}$$ 
y^2 - b^2 + 7*b*y
Numerical answer [src] 
y^2 - b^2 + 7.0*b*y
y^2 - b^2 + 7.0*b*y
Combining rational expressions [src] 
   2              
- b  + y*(y + 7*b)
$$- b^{2} + y \left(7 b + y\right)$$ 
-b^2 + y*(y + 7*b)
Trigonometric part [src] 
 2    2        
y  - b  + 7*b*y
$$- b^{2} + 7 b y + y^{2}$$ 
y^2 - b^2 + 7*b*y
Assemble expression [src] 
 2    2        
y  - b  + 7*b*y
$$- b^{2} + 7 b y + y^{2}$$ 
y^2 - b^2 + 7*b*y
Rational denominator [src] 
 2    2        
y  - b  + 7*b*y
$$- b^{2} + 7 b y + y^{2}$$ 
y^2 - b^2 + 7*b*y
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