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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−3- y^{2} - y - 3 
-3 - y - y^2
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)
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}
Combining rational expressions [src] 
-3 + y*(-1 - y)
y(−y−1)−3y \left(- y - 1\right) - 3 
-3 + y*(-1 - y)
Powers [src] 
          2
-3 - y - y
−y2−y−3- y^{2} - y - 3 
-3 - y - y^2
Assemble expression [src] 
          2
-3 - y - y
−y2−y−3- y^{2} - y - 3 
-3 - y - y^2
Numerical answer [src] 
-3.0 - y - y^2
-3.0 - y - y^2
Trigonometric part [src] 
          2
-3 - y - y
−y2−y−3- y^{2} - y - 3 
-3 - y - y^2
Rational denominator [src] 
          2
-3 - y - y
−y2−y−3- y^{2} - y - 3 
-3 - y - y^2
Common denominator [src] 
          2
-3 - y - y
−y2−y−3- y^{2} - y - 3 
-3 - y - y^2
Combinatorics [src] 
          2
-3 - y - y
−y2−y−3- y^{2} - y - 3 
-3 - y - y^2
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