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Factor -y^4-y^2+3 squared

An expression to simplify:

The solution

You have entered [src]
   4    2    
- y  - y  + 3
$$\left(- y^{4} - y^{2}\right) + 3$$
-y^4 - y^2 + 3
General simplification [src]
     2    4
3 - y  - y 
$$- y^{4} - y^{2} + 3$$
3 - y^2 - y^4
The perfect square
Let's highlight the perfect square of the square three-member
$$\left(- y^{4} - y^{2}\right) + 3$$
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
$$a = -1$$
$$b = -1$$
$$c = 3$$
Then
$$m = \frac{1}{2}$$
$$n = \frac{13}{4}$$
So,
$$\frac{13}{4} - \left(y^{2} + \frac{1}{2}\right)^{2}$$
Factorization [src]
/           ____________\ /           ____________\ /         ______________\ /         ______________\
|          /       ____ | |          /       ____ | |        /         ____ | |        /         ____ |
|         /  1   \/ 13  | |         /  1   \/ 13  | |       /    1   \/ 13  | |       /    1   \/ 13  |
|x + I*  /   - + ------ |*|x - I*  /   - + ------ |*|x +   /   - - + ------ |*|x -   /   - - + ------ |
\      \/    2     2    / \      \/    2     2    / \    \/      2     2    / \    \/      2     2    /
$$\left(x - i \sqrt{\frac{1}{2} + \frac{\sqrt{13}}{2}}\right) \left(x + i \sqrt{\frac{1}{2} + \frac{\sqrt{13}}{2}}\right) \left(x + \sqrt{- \frac{1}{2} + \frac{\sqrt{13}}{2}}\right) \left(x - \sqrt{- \frac{1}{2} + \frac{\sqrt{13}}{2}}\right)$$
(((x + i*sqrt(1/2 + sqrt(13)/2))*(x - i*sqrt(1/2 + sqrt(13)/2)))*(x + sqrt(-1/2 + sqrt(13)/2)))*(x - sqrt(-1/2 + sqrt(13)/2))
Trigonometric part [src]
     2    4
3 - y  - y 
$$- y^{4} - y^{2} + 3$$
3 - y^2 - y^4
Numerical answer [src]
3.0 - y^2 - y^4
3.0 - y^2 - y^4
Assemble expression [src]
     2    4
3 - y  - y 
$$- y^{4} - y^{2} + 3$$
3 - y^2 - y^4
Powers [src]
     2    4
3 - y  - y 
$$- y^{4} - y^{2} + 3$$
3 - y^2 - y^4
Combinatorics [src]
     2    4
3 - y  - y 
$$- y^{4} - y^{2} + 3$$
3 - y^2 - y^4
Combining rational expressions [src]
     2 /      2\
3 + y *\-1 - y /
$$y^{2} \left(- y^{2} - 1\right) + 3$$
3 + y^2*(-1 - y^2)
Rational denominator [src]
     2    4
3 - y  - y 
$$- y^{4} - y^{2} + 3$$
3 - y^2 - y^4
Common denominator [src]
     2    4
3 - y  - y 
$$- y^{4} - y^{2} + 3$$
3 - y^2 - y^4