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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
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}
Factorization [src] 
/          ____\ /          ____\
|    1   \/ 13 | |    1   \/ 13 |
|x + - - ------|*|x + - + ------|
\    2     2   / \    2     2   /
(x+(12−132))(x+(12+132))\left(x + \left(\frac{1}{2} - \frac{\sqrt{13}}{2}\right)\right) \left(x + \left(\frac{1}{2} + \frac{\sqrt{13}}{2}\right)\right) 
(x + 1/2 - sqrt(13)/2)*(x + 1/2 + sqrt(13)/2)
General simplification [src] 
          2
-3 + y + y
y2+y−3y^{2} + y - 3 
-3 + y + y^2
Rational denominator [src] 
          2
-3 + y + y
y2+y−3y^{2} + y - 3 
-3 + y + y^2
Trigonometric part [src] 
          2
-3 + y + y
y2+y−3y^{2} + y - 3 
-3 + y + y^2
Assemble expression [src] 
          2
-3 + y + y
y2+y−3y^{2} + y - 3 
-3 + y + y^2
Common denominator [src] 
          2
-3 + y + y
y2+y−3y^{2} + y - 3 
-3 + y + y^2
Powers [src] 
          2
-3 + y + y
y2+y−3y^{2} + y - 3 
-3 + y + y^2
Combinatorics [src] 
          2
-3 + y + y
y2+y−3y^{2} + y - 3 
-3 + y + y^2
Numerical answer [src] 
-3.0 + y + y^2
-3.0 + y + y^2
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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