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Expression simplification/ Factor perfect squares/ -y^2-4*y*b+14*b^2

Factor -y^2-4*y*b+14*b^2 squared

An expression to simplify:

The solution

You have entered [src] 
   2               2
- y  - 4*y*b + 14*b
$$14 b^{2} + \left(- b 4 y - y^{2}\right)$$ 
-y^2 - 4*y*b + 14*b^2
The perfect square
Let's highlight the perfect square of the square three-member
$$14 b^{2} + \left(- b 4 y - y^{2}\right)$$
Let us write down the identical expression
$$14 b^{2} + \left(- b 4 y - y^{2}\right) = - \frac{9 y^{2}}{7} + \left(14 b^{2} - 4 b y + \frac{2 y^{2}}{7}\right)$$
or
$$14 b^{2} + \left(- b 4 y - y^{2}\right) = - \frac{9 y^{2}}{7} + \left(\sqrt{14} b - \frac{\sqrt{14} y}{7}\right)^{2}$$
in the view of the product
$$\left(- \sqrt{\frac{9}{7}} y + \left(\sqrt{14} b + - \frac{\sqrt{14}}{7} y\right)\right) \left(\sqrt{\frac{9}{7}} y + \left(\sqrt{14} b + - \frac{\sqrt{14}}{7} y\right)\right)$$
$$\left(- \frac{3 \sqrt{7}}{7} y + \left(\sqrt{14} b + - \frac{\sqrt{14}}{7} y\right)\right) \left(\frac{3 \sqrt{7}}{7} y + \left(\sqrt{14} b + - \frac{\sqrt{14}}{7} y\right)\right)$$
$$\left(\sqrt{14} b + y \left(- \frac{\sqrt{14}}{7} + \frac{3 \sqrt{7}}{7}\right)\right) \left(\sqrt{14} b + y \left(- \frac{3 \sqrt{7}}{7} - \frac{\sqrt{14}}{7}\right)\right)$$
$$\left(\sqrt{14} b + y \left(- \frac{\sqrt{14}}{7} + \frac{3 \sqrt{7}}{7}\right)\right) \left(\sqrt{14} b + y \left(- \frac{3 \sqrt{7}}{7} - \frac{\sqrt{14}}{7}\right)\right)$$
Factorization [src] 
/      /        ___\\ /      /        ___\\
|    y*\2 - 3*\/ 2 /| |    y*\2 + 3*\/ 2 /|
|b - ---------------|*|b - ---------------|
\           14      / \           14      /
$$\left(b - \frac{y \left(2 - 3 \sqrt{2}\right)}{14}\right) \left(b - \frac{y \left(2 + 3 \sqrt{2}\right)}{14}\right)$$ 
(b - y*(2 - 3*sqrt(2))/14)*(b - y*(2 + 3*sqrt(2))/14)
General simplification [src] 
   2       2        
- y  + 14*b  - 4*b*y
$$14 b^{2} - 4 b y - y^{2}$$ 
-y^2 + 14*b^2 - 4*b*y
Powers [src] 
   2       2        
- y  + 14*b  - 4*b*y
$$14 b^{2} - 4 b y - y^{2}$$ 
-y^2 + 14*b^2 - 4*b*y
Trigonometric part [src] 
   2       2        
- y  + 14*b  - 4*b*y
$$14 b^{2} - 4 b y - y^{2}$$ 
-y^2 + 14*b^2 - 4*b*y
Numerical answer [src] 
-y^2 + 14.0*b^2 - 4.0*b*y
-y^2 + 14.0*b^2 - 4.0*b*y
Combining rational expressions [src] 
    2               
14*b  + y*(-y - 4*b)
$$14 b^{2} + y \left(- 4 b - y\right)$$ 
14*b^2 + y*(-y - 4*b)
Common denominator [src] 
   2       2        
- y  + 14*b  - 4*b*y
$$14 b^{2} - 4 b y - y^{2}$$ 
-y^2 + 14*b^2 - 4*b*y
Assemble expression [src] 
   2       2        
- y  + 14*b  - 4*b*y
$$14 b^{2} - 4 b y - y^{2}$$ 
-y^2 + 14*b^2 - 4*b*y
Rational denominator [src] 
   2       2        
- y  + 14*b  - 4*b*y
$$14 b^{2} - 4 b y - y^{2}$$ 
-y^2 + 14*b^2 - 4*b*y
Combinatorics [src] 
   2       2        
- y  + 14*b  - 4*b*y
$$14 b^{2} - 4 b y - y^{2}$$ 
-y^2 + 14*b^2 - 4*b*y
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