Mister Exam
Factor -y^4-4*y^2+2 squared
The solution
The perfect square
Let's highlight the perfect square of the square three-member
$$\left(- y^{4} - 4 y^{2}\right) + 2$$
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
$$a = -1$$
$$b = -4$$
$$c = 2$$
Then
$$m = 2$$
$$n = 6$$
So,
$$6 - \left(y^{2} + 2\right)^{2}$$
$$\left(- y^{4} - 4 y^{2}\right) + 2$$
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
$$a = -1$$
$$b = -4$$
$$c = 2$$
Then
$$m = 2$$
$$n = 6$$
So,
$$6 - \left(y^{2} + 2\right)^{2}$$
Factorization
[src]
/ ___________\ / ___________\ / ____________\ / ____________\ | / ___ | | / ___ | | / ___ | | / ___ | \x + I*\/ 2 + \/ 6 /*\x - I*\/ 2 + \/ 6 /*\x + \/ -2 + \/ 6 /*\x - \/ -2 + \/ 6 /
$$\left(x - i \sqrt{2 + \sqrt{6}}\right) \left(x + i \sqrt{2 + \sqrt{6}}\right) \left(x + \sqrt{-2 + \sqrt{6}}\right) \left(x - \sqrt{-2 + \sqrt{6}}\right)$$
(((x + i*sqrt(2 + sqrt(6)))*(x - i*sqrt(2 + sqrt(6))))*(x + sqrt(-2 + sqrt(6))))*(x - sqrt(-2 + sqrt(6)))
Combining rational expressions
[src]
2 / 2\ 2 + y *\-4 - y /
$$y^{2} \left(- y^{2} - 4\right) + 2$$
2 + y^2*(-4 - y^2)