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