Mister Exam
Factor y^4+9*y^2+8 squared
The solution
Factorization
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/ ___\ / ___\ (x + I)*(x - I)*\x + 2*I*\/ 2 /*\x - 2*I*\/ 2 /
$$\left(x - i\right) \left(x + i\right) \left(x + 2 \sqrt{2} i\right) \left(x - 2 \sqrt{2} i\right)$$
(((x + i)*(x - i))*(x + 2*i*sqrt(2)))*(x - 2*i*sqrt(2))
The perfect square
Let's highlight the perfect square of the square three-member
$$\left(y^{4} + 9 y^{2}\right) + 8$$
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
$$a = 1$$
$$b = 9$$
$$c = 8$$
Then
$$m = \frac{9}{2}$$
$$n = - \frac{49}{4}$$
So,
$$\left(y^{2} + \frac{9}{2}\right)^{2} - \frac{49}{4}$$
$$\left(y^{4} + 9 y^{2}\right) + 8$$
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
$$a = 1$$
$$b = 9$$
$$c = 8$$
Then
$$m = \frac{9}{2}$$
$$n = - \frac{49}{4}$$
So,
$$\left(y^{2} + \frac{9}{2}\right)^{2} - \frac{49}{4}$$
Combinatorics
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/ 2\ / 2\ \1 + y /*\8 + y /
$$\left(y^{2} + 1\right) \left(y^{2} + 8\right)$$
(1 + y^2)*(8 + y^2)
Combining rational expressions
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2 / 2\ 8 + y *\9 + y /
$$y^{2} \left(y^{2} + 9\right) + 8$$
8 + y^2*(9 + y^2)