Mister Exam
Factor -y^4+4*y^2-4 squared
The solution
Factorization
[src]
/ ___\ / ___\ \x + \/ 2 /*\x - \/ 2 /
$$\left(x - \sqrt{2}\right) \left(x + \sqrt{2}\right)$$
(x + sqrt(2))*(x - sqrt(2))
The perfect square
Let's highlight the perfect square of the square three-member
$$\left(- y^{4} + 4 y^{2}\right) - 4$$
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
$$a = -1$$
$$b = 4$$
$$c = -4$$
Then
$$m = -2$$
$$n = 0$$
So,
$$- \left(y^{2} - 2\right)^{2}$$
$$\left(- y^{4} + 4 y^{2}\right) - 4$$
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
$$a = -1$$
$$b = 4$$
$$c = -4$$
Then
$$m = -2$$
$$n = 0$$
So,
$$- \left(y^{2} - 2\right)^{2}$$
Combining rational expressions
[src]
2 / 2\ -4 + y *\4 - y /
$$y^{2} \left(4 - y^{2}\right) - 4$$
-4 + y^2*(4 - y^2)