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Expression simplification/ Factor perfect squares/ y^2+5*y*b+6*b^2

Factor y^2+5*y*b+6*b^2 squared

An expression to simplify:

The solution

You have entered [src] 
 2              2
y  + 5*y*b + 6*b
$$6 b^{2} + \left(b 5 y + y^{2}\right)$$ 
y^2 + (5*y)*b + 6*b^2
The perfect square
Let's highlight the perfect square of the square three-member
$$6 b^{2} + \left(b 5 y + y^{2}\right)$$
Let us write down the identical expression
$$6 b^{2} + \left(b 5 y + y^{2}\right) = - \frac{y^{2}}{24} + \left(6 b^{2} + 5 b y + \frac{25 y^{2}}{24}\right)$$
or
$$6 b^{2} + \left(b 5 y + y^{2}\right) = - \frac{y^{2}}{24} + \left(\sqrt{6} b + \frac{5 \sqrt{6} y}{12}\right)^{2}$$
in the view of the product
$$\left(- \frac{y}{2 \sqrt{6}} + \left(\sqrt{6} b + \frac{5 \sqrt{6}}{12} y\right)\right) \left(\frac{y}{2 \sqrt{6}} + \left(\sqrt{6} b + \frac{5 \sqrt{6}}{12} y\right)\right)$$
$$\left(- \frac{\sqrt{6}}{12} y + \left(\sqrt{6} b + \frac{5 \sqrt{6}}{12} y\right)\right) \left(\frac{\sqrt{6}}{12} y + \left(\sqrt{6} b + \frac{5 \sqrt{6}}{12} y\right)\right)$$
$$\left(\sqrt{6} b + y \left(- \frac{\sqrt{6}}{12} + \frac{5 \sqrt{6}}{12}\right)\right) \left(\sqrt{6} b + y \left(\frac{\sqrt{6}}{12} + \frac{5 \sqrt{6}}{12}\right)\right)$$
$$\left(\sqrt{6} b + \frac{\sqrt{6} y}{3}\right) \left(\sqrt{6} b + \frac{\sqrt{6} y}{2}\right)$$
Factorization [src] 
/    y\ /    y\
|b + -|*|b + -|
\    2/ \    3/
$$\left(b + \frac{y}{3}\right) \left(b + \frac{y}{2}\right)$$ 
(b + y/2)*(b + y/3)
General simplification [src] 
 2      2        
y  + 6*b  + 5*b*y
$$6 b^{2} + 5 b y + y^{2}$$ 
y^2 + 6*b^2 + 5*b*y
Assemble expression [src] 
 2      2        
y  + 6*b  + 5*b*y
$$6 b^{2} + 5 b y + y^{2}$$ 
y^2 + 6*b^2 + 5*b*y
Common denominator [src] 
 2      2        
y  + 6*b  + 5*b*y
$$6 b^{2} + 5 b y + y^{2}$$ 
y^2 + 6*b^2 + 5*b*y
Combinatorics [src] 
(y + 2*b)*(y + 3*b)
$$\left(2 b + y\right) \left(3 b + y\right)$$ 
(y + 2*b)*(y + 3*b)
Numerical answer [src] 
y^2 + 6.0*b^2 + 5.0*b*y
y^2 + 6.0*b^2 + 5.0*b*y
Combining rational expressions [src] 
   2              
6*b  + y*(y + 5*b)
$$6 b^{2} + y \left(5 b + y\right)$$ 
6*b^2 + y*(y + 5*b)
Powers [src] 
 2      2        
y  + 6*b  + 5*b*y
$$6 b^{2} + 5 b y + y^{2}$$ 
y^2 + 6*b^2 + 5*b*y
Rational denominator [src] 
 2      2        
y  + 6*b  + 5*b*y
$$6 b^{2} + 5 b y + y^{2}$$ 
y^2 + 6*b^2 + 5*b*y
Trigonometric part [src] 
 2      2        
y  + 6*b  + 5*b*y
$$6 b^{2} + 5 b y + y^{2}$$ 
y^2 + 6*b^2 + 5*b*y
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