Mister Exam
Factor -y^4-4*y^2+5 squared
The solution
Factorization
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/ ___\ / ___\ (x + 1)*(x - 1)*\x + I*\/ 5 /*\x - I*\/ 5 /
$$\left(x - 1\right) \left(x + 1\right) \left(x + \sqrt{5} i\right) \left(x - \sqrt{5} i\right)$$
(((x + 1)*(x - 1))*(x + i*sqrt(5)))*(x - i*sqrt(5))
The perfect square
Let's highlight the perfect square of the square three-member
$$\left(- y^{4} - 4 y^{2}\right) + 5$$
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
$$a = -1$$
$$b = -4$$
$$c = 5$$
Then
$$m = 2$$
$$n = 9$$
So,
$$9 - \left(y^{2} + 2\right)^{2}$$
$$\left(- y^{4} - 4 y^{2}\right) + 5$$
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
$$a = -1$$
$$b = -4$$
$$c = 5$$
Then
$$m = 2$$
$$n = 9$$
So,
$$9 - \left(y^{2} + 2\right)^{2}$$
Combinatorics
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/ 2\ -(1 + y)*(-1 + y)*\5 + y /
$$- \left(y - 1\right) \left(y + 1\right) \left(y^{2} + 5\right)$$
-(1 + y)*(-1 + y)*(5 + y^2)
Combining rational expressions
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2 / 2\ 5 + y *\-4 - y /
$$y^{2} \left(- y^{2} - 4\right) + 5$$
5 + y^2*(-4 - y^2)