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Expression simplification/ Factor perfect squares/ -y^4-13*y^2+2

Factor -y^4-13*y^2+2 squared

An expression to simplify:

The solution

You have entered [src] 
   4       2    
- y  - 13*y  + 2
$$\left(- y^{4} - 13 y^{2}\right) + 2$$ 
-y^4 - 13*y^2 + 2
General simplification [src] 
     4       2
2 - y  - 13*y
$$- y^{4} - 13 y^{2} + 2$$ 
2 - y^4 - 13*y^2
The perfect square
Let's highlight the perfect square of the square three-member
$$\left(- y^{4} - 13 y^{2}\right) + 2$$
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
$$a = -1$$
$$b = -13$$
$$c = 2$$
Then
$$m = \frac{13}{2}$$
$$n = \frac{177}{4}$$
So,
$$\frac{177}{4} - \left(y^{2} + \frac{13}{2}\right)^{2}$$
Factorization [src] 
/           ______________\ /           ______________\ /         ________________\ /         ________________\
|          /        _____ | |          /        _____ | |        /          _____ | |        /          _____ |
|         /  13   \/ 177  | |         /  13   \/ 177  | |       /    13   \/ 177  | |       /    13   \/ 177  |
|x + I*  /   -- + ------- |*|x - I*  /   -- + ------- |*|x +   /   - -- + ------- |*|x -   /   - -- + ------- |
\      \/    2       2    / \      \/    2       2    / \    \/      2       2    / \    \/      2       2    /
$$\left(x - i \sqrt{\frac{13}{2} + \frac{\sqrt{177}}{2}}\right) \left(x + i \sqrt{\frac{13}{2} + \frac{\sqrt{177}}{2}}\right) \left(x + \sqrt{- \frac{13}{2} + \frac{\sqrt{177}}{2}}\right) \left(x - \sqrt{- \frac{13}{2} + \frac{\sqrt{177}}{2}}\right)$$ 
(((x + i*sqrt(13/2 + sqrt(177)/2))*(x - i*sqrt(13/2 + sqrt(177)/2)))*(x + sqrt(-13/2 + sqrt(177)/2)))*(x - sqrt(-13/2 + sqrt(177)/2))
Numerical answer [src] 
2.0 - y^4 - 13.0*y^2
2.0 - y^4 - 13.0*y^2
Combining rational expressions [src] 
     2 /       2\
2 + y *\-13 - y /
$$y^{2} \left(- y^{2} - 13\right) + 2$$ 
2 + y^2*(-13 - y^2)
Powers [src] 
     4       2
2 - y  - 13*y
$$- y^{4} - 13 y^{2} + 2$$ 
2 - y^4 - 13*y^2
Common denominator [src] 
     4       2
2 - y  - 13*y
$$- y^{4} - 13 y^{2} + 2$$ 
2 - y^4 - 13*y^2
Trigonometric part [src] 
     4       2
2 - y  - 13*y
$$- y^{4} - 13 y^{2} + 2$$ 
2 - y^4 - 13*y^2
Rational denominator [src] 
     4       2
2 - y  - 13*y
$$- y^{4} - 13 y^{2} + 2$$ 
2 - y^4 - 13*y^2
Combinatorics [src] 
     4       2
2 - y  - 13*y
$$- y^{4} - 13 y^{2} + 2$$ 
2 - y^4 - 13*y^2
Assemble expression [src] 
     4       2
2 - y  - 13*y
$$- y^{4} - 13 y^{2} + 2$$ 
2 - y^4 - 13*y^2
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