Mister Exam
Factor -y^4-8*y^2+9 squared
The solution
Factorization
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(x + 1)*(x - 1)*(x + 3*I)*(x - 3*I)
$$\left(x - 1\right) \left(x + 1\right) \left(x + 3 i\right) \left(x - 3 i\right)$$
(((x + 1)*(x - 1))*(x + 3*i))*(x - 3*i)
The perfect square
Let's highlight the perfect square of the square three-member
$$\left(- y^{4} - 8 y^{2}\right) + 9$$
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
$$a = -1$$
$$b = -8$$
$$c = 9$$
Then
$$m = 4$$
$$n = 25$$
So,
$$25 - \left(y^{2} + 4\right)^{2}$$
$$\left(- y^{4} - 8 y^{2}\right) + 9$$
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
$$a = -1$$
$$b = -8$$
$$c = 9$$
Then
$$m = 4$$
$$n = 25$$
So,
$$25 - \left(y^{2} + 4\right)^{2}$$
Combining rational expressions
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2 / 2\ 9 + y *\-8 - y /
$$y^{2} \left(- y^{2} - 8\right) + 9$$
9 + y^2*(-8 - y^2)
Combinatorics
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/ 2\ -(1 + y)*(-1 + y)*\9 + y /
$$- \left(y - 1\right) \left(y + 1\right) \left(y^{2} + 9\right)$$
-(1 + y)*(-1 + y)*(9 + y^2)