Mister Exam
Factor -y^4-14*y^2-2 squared
The solution
Factorization
[src]
/ ____________\ / ____________\ / ____________\ / ____________\ | / ____ | | / ____ | | / ____ | | / ____ | \x + I*\/ 7 - \/ 47 /*\x - I*\/ 7 - \/ 47 /*\x + I*\/ 7 + \/ 47 /*\x - I*\/ 7 + \/ 47 /
$$\left(x - i \sqrt{7 - \sqrt{47}}\right) \left(x + i \sqrt{7 - \sqrt{47}}\right) \left(x + i \sqrt{\sqrt{47} + 7}\right) \left(x - i \sqrt{\sqrt{47} + 7}\right)$$
(((x + i*sqrt(7 - sqrt(47)))*(x - i*sqrt(7 - sqrt(47))))*(x + i*sqrt(7 + sqrt(47))))*(x - i*sqrt(7 + sqrt(47)))
The perfect square
Let's highlight the perfect square of the square three-member
$$\left(- y^{4} - 14 y^{2}\right) - 2$$
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
$$a = -1$$
$$b = -14$$
$$c = -2$$
Then
$$m = 7$$
$$n = 47$$
So,
$$47 - \left(y^{2} + 7\right)^{2}$$
$$\left(- y^{4} - 14 y^{2}\right) - 2$$
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
$$a = -1$$
$$b = -14$$
$$c = -2$$
Then
$$m = 7$$
$$n = 47$$
So,
$$47 - \left(y^{2} + 7\right)^{2}$$
Combining rational expressions
[src]
2 / 2\ -2 + y *\-14 - y /
$$y^{2} \left(- y^{2} - 14\right) - 2$$
-2 + y^2*(-14 - y^2)