Mister Exam
Factor -y^4-10*y^2-2 squared
The solution
The perfect square
Let's highlight the perfect square of the square three-member
$$\left(- y^{4} - 10 y^{2}\right) - 2$$
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
$$a = -1$$
$$b = -10$$
$$c = -2$$
Then
$$m = 5$$
$$n = 23$$
So,
$$23 - \left(y^{2} + 5\right)^{2}$$
$$\left(- y^{4} - 10 y^{2}\right) - 2$$
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
$$a = -1$$
$$b = -10$$
$$c = -2$$
Then
$$m = 5$$
$$n = 23$$
So,
$$23 - \left(y^{2} + 5\right)^{2}$$
Factorization
[src]
/ ____________\ / ____________\ / ____________\ / ____________\ | / ____ | | / ____ | | / ____ | | / ____ | \x + I*\/ 5 - \/ 23 /*\x - I*\/ 5 - \/ 23 /*\x + I*\/ 5 + \/ 23 /*\x - I*\/ 5 + \/ 23 /
$$\left(x - i \sqrt{5 - \sqrt{23}}\right) \left(x + i \sqrt{5 - \sqrt{23}}\right) \left(x + i \sqrt{\sqrt{23} + 5}\right) \left(x - i \sqrt{\sqrt{23} + 5}\right)$$
(((x + i*sqrt(5 - sqrt(23)))*(x - i*sqrt(5 - sqrt(23))))*(x + i*sqrt(5 + sqrt(23))))*(x - i*sqrt(5 + sqrt(23)))
Combining rational expressions
[src]
2 / 2\ -2 + y *\-10 - y /
$$y^{2} \left(- y^{2} - 10\right) - 2$$
-2 + y^2*(-10 - y^2)