Mister Exam
Factor y^4+4*y^2-13 squared
The solution
Factorization
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/ ____________\ / ____________\ / _____________\ / _____________\ | / ____ | | / ____ | | / ____ | | / ____ | \x + I*\/ 2 + \/ 17 /*\x - I*\/ 2 + \/ 17 /*\x + \/ -2 + \/ 17 /*\x - \/ -2 + \/ 17 /
$$\left(x - i \sqrt{2 + \sqrt{17}}\right) \left(x + i \sqrt{2 + \sqrt{17}}\right) \left(x + \sqrt{-2 + \sqrt{17}}\right) \left(x - \sqrt{-2 + \sqrt{17}}\right)$$
(((x + i*sqrt(2 + sqrt(17)))*(x - i*sqrt(2 + sqrt(17))))*(x + sqrt(-2 + sqrt(17))))*(x - sqrt(-2 + sqrt(17)))
The perfect square
Let's highlight the perfect square of the square three-member
$$\left(y^{4} + 4 y^{2}\right) - 13$$
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
$$a = 1$$
$$b = 4$$
$$c = -13$$
Then
$$m = 2$$
$$n = -17$$
So,
$$\left(y^{2} + 2\right)^{2} - 17$$
$$\left(y^{4} + 4 y^{2}\right) - 13$$
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
$$a = 1$$
$$b = 4$$
$$c = -13$$
Then
$$m = 2$$
$$n = -17$$
So,
$$\left(y^{2} + 2\right)^{2} - 17$$
Combining rational expressions
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2 / 2\ -13 + y *\4 + y /
$$y^{2} \left(y^{2} + 4\right) - 13$$
-13 + y^2*(4 + y^2)