Mister Exam

Factor y^2-y-4 squared

An expression to simplify:

The solution

You have entered [src]
 2        
y  - y - 4
$$\left(y^{2} - y\right) - 4$$
y^2 - y - 4
The perfect square
Let's highlight the perfect square of the square three-member
$$\left(y^{2} - y\right) - 4$$
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
$$a = 1$$
$$b = -1$$
$$c = -4$$
Then
$$m = - \frac{1}{2}$$
$$n = - \frac{17}{4}$$
So,
$$\left(y - \frac{1}{2}\right)^{2} - \frac{17}{4}$$
General simplification [src]
      2    
-4 + y  - y
$$y^{2} - y - 4$$
-4 + y^2 - y
Factorization [src]
/            ____\ /            ____\
|      1   \/ 17 | |      1   \/ 17 |
|x + - - + ------|*|x + - - - ------|
\      2     2   / \      2     2   /
$$\left(x + \left(- \frac{1}{2} + \frac{\sqrt{17}}{2}\right)\right) \left(x + \left(- \frac{\sqrt{17}}{2} - \frac{1}{2}\right)\right)$$
(x - 1/2 + sqrt(17)/2)*(x - 1/2 - sqrt(17)/2)
Trigonometric part [src]
      2    
-4 + y  - y
$$y^{2} - y - 4$$
-4 + y^2 - y
Powers [src]
      2    
-4 + y  - y
$$y^{2} - y - 4$$
-4 + y^2 - y
Combinatorics [src]
      2    
-4 + y  - y
$$y^{2} - y - 4$$
-4 + y^2 - y
Rational denominator [src]
      2    
-4 + y  - y
$$y^{2} - y - 4$$
-4 + y^2 - y
Common denominator [src]
      2    
-4 + y  - y
$$y^{2} - y - 4$$
-4 + y^2 - y
Numerical answer [src]
-4.0 + y^2 - y
-4.0 + y^2 - y
Assemble expression [src]
      2    
-4 + y  - y
$$y^{2} - y - 4$$
-4 + y^2 - y
Combining rational expressions [src]
-4 + y*(-1 + y)
$$y \left(y - 1\right) - 4$$
-4 + y*(-1 + y)