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
General simplification [src]
         2
4 + y + y 
$$y^{2} + y + 4$$
4 + y + y^2
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
$$m = \frac{1}{2}$$
$$n = \frac{15}{4}$$
So,
$$\left(y + \frac{1}{2}\right)^{2} + \frac{15}{4}$$
Factorization [src]
/            ____\ /            ____\
|    1   I*\/ 15 | |    1   I*\/ 15 |
|x + - + --------|*|x + - - --------|
\    2      2    / \    2      2    /
$$\left(x + \left(\frac{1}{2} - \frac{\sqrt{15} i}{2}\right)\right) \left(x + \left(\frac{1}{2} + \frac{\sqrt{15} i}{2}\right)\right)$$
(x + 1/2 + i*sqrt(15)/2)*(x + 1/2 - i*sqrt(15)/2)
Trigonometric part [src]
         2
4 + y + y 
$$y^{2} + y + 4$$
4 + y + y^2
Common denominator [src]
         2
4 + y + y 
$$y^{2} + y + 4$$
4 + y + y^2
Assemble expression [src]
         2
4 + y + y 
$$y^{2} + y + 4$$
4 + y + y^2
Powers [src]
         2
4 + y + y 
$$y^{2} + y + 4$$
4 + y + y^2
Rational denominator [src]
         2
4 + y + y 
$$y^{2} + y + 4$$
4 + y + y^2
Combinatorics [src]
         2
4 + y + y 
$$y^{2} + y + 4$$
4 + y + y^2
Numerical answer [src]
4.0 + y + y^2
4.0 + y + y^2
Combining rational expressions [src]
4 + y*(1 + y)
$$y \left(y + 1\right) + 4$$
4 + y*(1 + y)