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Expression simplification/ Factor perfect squares/ -y^2-7*y*b-5*b^2

Factor -y^2-7*y*b-5*b^2 squared

An expression to simplify:

The solution

You have entered [src] 
   2              2
- y  - 7*y*b - 5*b
$$- 5 b^{2} + \left(- b 7 y - y^{2}\right)$$ 
-y^2 - 7*y*b - 5*b^2
General simplification [src] 
   2      2        
- y  - 5*b  - 7*b*y
$$- 5 b^{2} - 7 b y - y^{2}$$ 
-y^2 - 5*b^2 - 7*b*y
Factorization [src] 
/      /       ____\\ /      /      ____\\
|    y*\-7 + \/ 29 /| |    y*\7 + \/ 29 /|
|b - ---------------|*|b + --------------|
\           10      / \          10      /
$$\left(b - \frac{y \left(-7 + \sqrt{29}\right)}{10}\right) \left(b + \frac{y \left(\sqrt{29} + 7\right)}{10}\right)$$ 
(b - y*(-7 + sqrt(29))/10)*(b + y*(7 + sqrt(29))/10)
The perfect square
Let's highlight the perfect square of the square three-member
$$- 5 b^{2} + \left(- b 7 y - y^{2}\right)$$
Let us write down the identical expression
$$- 5 b^{2} + \left(- b 7 y - y^{2}\right) = \frac{29 y^{2}}{20} + \left(- 5 b^{2} - 7 b y - \frac{49 y^{2}}{20}\right)$$
or
$$- 5 b^{2} + \left(- b 7 y - y^{2}\right) = \frac{29 y^{2}}{20} - \left(\sqrt{5} b + \frac{7 \sqrt{5} y}{10}\right)^{2}$$
Trigonometric part [src] 
   2      2        
- y  - 5*b  - 7*b*y
$$- 5 b^{2} - 7 b y - y^{2}$$ 
-y^2 - 5*b^2 - 7*b*y
Common denominator [src] 
   2      2        
- y  - 5*b  - 7*b*y
$$- 5 b^{2} - 7 b y - y^{2}$$ 
-y^2 - 5*b^2 - 7*b*y
Rational denominator [src] 
   2      2        
- y  - 5*b  - 7*b*y
$$- 5 b^{2} - 7 b y - y^{2}$$ 
-y^2 - 5*b^2 - 7*b*y
Combinatorics [src] 
   2      2        
- y  - 5*b  - 7*b*y
$$- 5 b^{2} - 7 b y - y^{2}$$ 
-y^2 - 5*b^2 - 7*b*y
Combining rational expressions [src] 
     2               
- 5*b  + y*(-y - 7*b)
$$- 5 b^{2} + y \left(- 7 b - y\right)$$ 
-5*b^2 + y*(-y - 7*b)
Numerical answer [src] 
-y^2 - 5.0*b^2 - 7.0*b*y
-y^2 - 5.0*b^2 - 7.0*b*y
Powers [src] 
   2      2        
- y  - 5*b  - 7*b*y
$$- 5 b^{2} - 7 b y - y^{2}$$ 
-y^2 - 5*b^2 - 7*b*y
Assemble expression [src] 
   2      2        
- y  - 5*b  - 7*b*y
$$- 5 b^{2} - 7 b y - y^{2}$$ 
-y^2 - 5*b^2 - 7*b*y
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