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Expression simplification/ Factor perfect squares/ y^2-y-3

Factor y^2-y-3 squared

An expression to simplify:

The solution

You have entered [src] 
 2        
y  - y - 3
(y2−y)−3\left(y^{2} - y\right) - 3 
y^2 - y - 3
General simplification [src] 
      2    
-3 + y  - y
y2−y−3y^{2} - y - 3 
-3 + y^2 - y
Factorization [src] 
/            ____\ /            ____\
|      1   \/ 13 | |      1   \/ 13 |
|x + - - + ------|*|x + - - - ------|
\      2     2   / \      2     2   /
(x+(−12+132))(x+(−132−12))\left(x + \left(- \frac{1}{2} + \frac{\sqrt{13}}{2}\right)\right) \left(x + \left(- \frac{\sqrt{13}}{2} - \frac{1}{2}\right)\right) 
(x - 1/2 + sqrt(13)/2)*(x - 1/2 - sqrt(13)/2)
The perfect square
Let's highlight the perfect square of the square three-member
(y2−y)−3\left(y^{2} - y\right) - 3
To do this, let's use the formula
ay2+by+c=a(m+y)2+na y^{2} + b y + c = a \left(m + y\right)^{2} + n
where
m=b2am = \frac{b}{2 a}
n=4ac−b24an = \frac{4 a c - b^{2}}{4 a}
In this case
a=1a = 1
b=−1b = -1
c=−3c = -3
Then
m=−12m = - \frac{1}{2}
n=−134n = - \frac{13}{4}
So,
(y−12)2−134\left(y - \frac{1}{2}\right)^{2} - \frac{13}{4}
Assemble expression [src] 
      2    
-3 + y  - y
y2−y−3y^{2} - y - 3 
-3 + y^2 - y
Rational denominator [src] 
      2    
-3 + y  - y
y2−y−3y^{2} - y - 3 
-3 + y^2 - y
Numerical answer [src] 
-3.0 + y^2 - y
-3.0 + y^2 - y
Combinatorics [src] 
      2    
-3 + y  - y
y2−y−3y^{2} - y - 3 
-3 + y^2 - y
Common denominator [src] 
      2    
-3 + y  - y
y2−y−3y^{2} - y - 3 
-3 + y^2 - y
Trigonometric part [src] 
      2    
-3 + y  - y
y2−y−3y^{2} - y - 3 
-3 + y^2 - y
Powers [src] 
      2    
-3 + y  - y
y2−y−3y^{2} - y - 3 
-3 + y^2 - y
Combining rational expressions [src] 
-3 + y*(-1 + y)
y(y−1)−3y \left(y - 1\right) - 3 
-3 + y*(-1 + y)
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