Mister Exam
Factor y^4-2*y^2-3 squared
The solution
The perfect square
Let's highlight the perfect square of the square three-member
$$\left(y^{4} - 2 y^{2}\right) - 3$$
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
$$a = 1$$
$$b = -2$$
$$c = -3$$
Then
$$m = -1$$
$$n = -4$$
So,
$$\left(y^{2} - 1\right)^{2} - 4$$
$$\left(y^{4} - 2 y^{2}\right) - 3$$
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
$$a = 1$$
$$b = -2$$
$$c = -3$$
Then
$$m = -1$$
$$n = -4$$
So,
$$\left(y^{2} - 1\right)^{2} - 4$$
Factorization
[src]
/ ___\ / ___\ \x + \/ 3 /*\x - \/ 3 /*(x + I)*(x - I)
$$\left(x - \sqrt{3}\right) \left(x + \sqrt{3}\right) \left(x + i\right) \left(x - i\right)$$
(((x + sqrt(3))*(x - sqrt(3)))*(x + i))*(x - i)
Combining rational expressions
[src]
2 / 2\ -3 + y *\-2 + y /
$$y^{2} \left(y^{2} - 2\right) - 3$$
-3 + y^2*(-2 + y^2)
Combinatorics
[src]
/ 2\ / 2\ \1 + y /*\-3 + y /
$$\left(y^{2} - 3\right) \left(y^{2} + 1\right)$$
(1 + y^2)*(-3 + y^2)