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

Factor -y^2+y+2 squared

An expression to simplify:

The solution

You have entered [src] 
   2        
- y  + y + 2
$$\left(- y^{2} + y\right) + 2$$ 
-y^2 + y + 2
General simplification [src] 
         2
2 + y - y
$$- y^{2} + y + 2$$ 
2 + y - y^2
Factorization [src] 
(x + 1)*(x - 2)
$$\left(x - 2\right) \left(x + 1\right)$$ 
(x + 1)*(x - 2)
The perfect square
Let's highlight the perfect square of the square three-member
$$\left(- y^{2} + y\right) + 2$$
To do this, let's use the formula
$$a y^{2} + b y + c = a \left(m + y\right)^{2} + n$$
where
$$m = \frac{b}{2 a}$$
$$n = \frac{4 a c - b^{2}}{4 a}$$
In this case
$$a = -1$$
$$b = 1$$
$$c = 2$$
Then
$$m = - \frac{1}{2}$$
$$n = \frac{9}{4}$$
So,
$$\frac{9}{4} - \left(y - \frac{1}{2}\right)^{2}$$
Numerical answer [src] 
2.0 + y - y^2
2.0 + y - y^2
Powers [src] 
         2
2 + y - y
$$- y^{2} + y + 2$$ 
2 + y - y^2
Assemble expression [src] 
         2
2 + y - y
$$- y^{2} + y + 2$$ 
2 + y - y^2
Trigonometric part [src] 
         2
2 + y - y
$$- y^{2} + y + 2$$ 
2 + y - y^2
Rational denominator [src] 
         2
2 + y - y
$$- y^{2} + y + 2$$ 
2 + y - y^2
Common denominator [src] 
         2
2 + y - y
$$- y^{2} + y + 2$$ 
2 + y - y^2
Combinatorics [src] 
-(1 + y)*(-2 + y)
$$- \left(y - 2\right) \left(y + 1\right)$$ 
-(1 + y)*(-2 + y)
Combining rational expressions [src] 
2 + y*(1 - y)
$$y \left(1 - y\right) + 2$$ 
2 + y*(1 - y)
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