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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
Factorization [src] 
/              ____\ /              ____\
|      1   I*\/ 11 | |      1   I*\/ 11 |
|x + - - + --------|*|x + - - - --------|
\      2      2    / \      2      2    /
(x+(−12−11i2))(x+(−12+11i2))\left(x + \left(- \frac{1}{2} - \frac{\sqrt{11} i}{2}\right)\right) \left(x + \left(- \frac{1}{2} + \frac{\sqrt{11} i}{2}\right)\right) 
(x - 1/2 + i*sqrt(11)/2)*(x - 1/2 - i*sqrt(11)/2)
General simplification [src] 
     2    
3 + y  - y
y2−y+3y^{2} - y + 3 
3 + y^2 - y
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=114n = \frac{11}{4}
So,
(y−12)2+114\left(y - \frac{1}{2}\right)^{2} + \frac{11}{4}
Rational denominator [src] 
     2    
3 + y  - y
y2−y+3y^{2} - y + 3 
3 + y^2 - y
Combinatorics [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
Assemble expression [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
Powers [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
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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