Mister Exam

Other calculators

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
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
$$m = \frac{1}{2}$$
$$n = - \frac{7}{4}$$
So,
$$- \left(y + \frac{1}{2}\right)^{2} - \frac{7}{4}$$
Factorization [src] 
/            ___\ /            ___\
|    1   I*\/ 7 | |    1   I*\/ 7 |
|x + - + -------|*|x + - - -------|
\    2      2   / \    2      2   /
$$\left(x + \left(\frac{1}{2} - \frac{\sqrt{7} i}{2}\right)\right) \left(x + \left(\frac{1}{2} + \frac{\sqrt{7} i}{2}\right)\right)$$ 
(x + 1/2 + i*sqrt(7)/2)*(x + 1/2 - i*sqrt(7)/2)
Numerical answer [src] 
-2.0 - y - y^2
-2.0 - y - y^2
Trigonometric part [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
Combining rational expressions [src] 
-2 + y*(-1 - y)
$$y \left(- y - 1\right) - 2$$ 
-2 + y*(-1 - y)
Common denominator [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
Powers [src] 
          2
-2 - y - y
$$- y^{2} - y - 2$$ 
-2 - y - y^2
Combinatorics [src] 
          2
-2 - y - y
$$- y^{2} - y - 2$$ 
-2 - y - y^2
    © Mister Exam – Calculator