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Expression simplification/ Factor perfect squares/ -y^4-y^2+6

Factor -y^4-y^2+6 squared

An expression to simplify:

The solution

You have entered [src] 
   4    2    
- y  - y  + 6
$$\left(- y^{4} - y^{2}\right) + 6$$ 
-y^4 - y^2 + 6
Factorization [src] 
/      ___\ /      ___\ /        ___\ /        ___\
\x + \/ 2 /*\x - \/ 2 /*\x + I*\/ 3 /*\x - I*\/ 3 /
$$\left(x - \sqrt{2}\right) \left(x + \sqrt{2}\right) \left(x + \sqrt{3} i\right) \left(x - \sqrt{3} i\right)$$ 
(((x + sqrt(2))*(x - sqrt(2)))*(x + i*sqrt(3)))*(x - i*sqrt(3))
The perfect square
Let's highlight the perfect square of the square three-member
$$\left(- y^{4} - y^{2}\right) + 6$$
To do this, let's use the formula
$$a y^{4} + b y^{2} + c = a \left(m + y^{2}\right)^{2} + n$$
where
$$m = \frac{b}{2 a}$$
$$n = \frac{4 a c - b^{2}}{4 a}$$
In this case
$$a = -1$$
$$b = -1$$
$$c = 6$$
Then
$$m = \frac{1}{2}$$
$$n = \frac{25}{4}$$
So,
$$\frac{25}{4} - \left(y^{2} + \frac{1}{2}\right)^{2}$$
General simplification [src] 
     2    4
6 - y  - y
$$- y^{4} - y^{2} + 6$$ 
6 - y^2 - y^4
Common denominator [src] 
     2    4
6 - y  - y
$$- y^{4} - y^{2} + 6$$ 
6 - y^2 - y^4
Assemble expression [src] 
     2    4
6 - y  - y
$$- y^{4} - y^{2} + 6$$ 
6 - y^2 - y^4
Numerical answer [src] 
6.0 - y^2 - y^4
6.0 - y^2 - y^4
Rational denominator [src] 
     2    4
6 - y  - y
$$- y^{4} - y^{2} + 6$$ 
6 - y^2 - y^4
Combinatorics [src] 
 /      2\ /     2\
-\-2 + y /*\3 + y /
$$- \left(y^{2} - 2\right) \left(y^{2} + 3\right)$$ 
-(-2 + y^2)*(3 + y^2)
Trigonometric part [src] 
     2    4
6 - y  - y
$$- y^{4} - y^{2} + 6$$ 
6 - y^2 - y^4
Powers [src] 
     2    4
6 - y  - y
$$- y^{4} - y^{2} + 6$$ 
6 - y^2 - y^4
Combining rational expressions [src] 
     2 /      2\
6 + y *\-1 - y /
$$y^{2} \left(- y^{2} - 1\right) + 6$$ 
6 + y^2*(-1 - y^2)
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