Mister Exam

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^2 - y
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,
$$\left(y - \frac{1}{2}\right)^{2} - \frac{9}{4}$$
Numerical answer [src]
-2.0 + y^2 - y
-2.0 + y^2 - y
Common denominator [src]
      2    
-2 + y  - y
$$y^{2} - y - 2$$
-2 + y^2 - y
Trigonometric part [src]
      2    
-2 + y  - y
$$y^{2} - y - 2$$
-2 + y^2 - y
Powers [src]
      2    
-2 + y  - y
$$y^{2} - y - 2$$
-2 + y^2 - y
Rational denominator [src]
      2    
-2 + y  - y
$$y^{2} - y - 2$$
-2 + y^2 - y
Assemble expression [src]
      2    
-2 + y  - y
$$y^{2} - y - 2$$
-2 + y^2 - y
Combining rational expressions [src]
-2 + y*(-1 + y)
$$y \left(y - 1\right) - 2$$
-2 + y*(-1 + y)
Combinatorics [src]
(1 + y)*(-2 + y)
$$\left(y - 2\right) \left(y + 1\right)$$
(1 + y)*(-2 + y)