Mister Exam
Factor -y^4-7*y^2-7 squared
The solution
Factorization
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$$\left(x - i \sqrt{\frac{7}{2} - \frac{\sqrt{21}}{2}}\right) \left(x + i \sqrt{\frac{7}{2} - \frac{\sqrt{21}}{2}}\right) \left(x + i \sqrt{\frac{\sqrt{21}}{2} + \frac{7}{2}}\right) \left(x - i \sqrt{\frac{\sqrt{21}}{2} + \frac{7}{2}}\right)$$
(((x + i*sqrt(7/2 - sqrt(21)/2))*(x - i*sqrt(7/2 - sqrt(21)/2)))*(x + i*sqrt(7/2 + sqrt(21)/2)))*(x - i*sqrt(7/2 + sqrt(21)/2))
The perfect square
Let's highlight the perfect square of the square three-member
$$\left(- y^{4} - 7 y^{2}\right) - 7$$
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
$$a = -1$$
$$b = -7$$
$$c = -7$$
Then
$$m = \frac{7}{2}$$
$$n = \frac{21}{4}$$
So,
$$\frac{21}{4} - \left(y^{2} + \frac{7}{2}\right)^{2}$$
$$\left(- y^{4} - 7 y^{2}\right) - 7$$
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
$$a = -1$$
$$b = -7$$
$$c = -7$$
Then
$$m = \frac{7}{2}$$
$$n = \frac{21}{4}$$
So,
$$\frac{21}{4} - \left(y^{2} + \frac{7}{2}\right)^{2}$$
Combining rational expressions
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2 / 2\ -7 + y *\-7 - y /
$$y^{2} \left(- y^{2} - 7\right) - 7$$
-7 + y^2*(-7 - y^2)