Mister Exam
Factor y^4-4*y^2-3 squared
The solution
The perfect square
Let's highlight the perfect square of the square three-member
$$\left(y^{4} - 4 y^{2}\right) - 3$$
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
$$a = 1$$
$$b = -4$$
$$c = -3$$
Then
$$m = -2$$
$$n = -7$$
So,
$$\left(y^{2} - 2\right)^{2} - 7$$
$$\left(y^{4} - 4 y^{2}\right) - 3$$
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
$$a = 1$$
$$b = -4$$
$$c = -3$$
Then
$$m = -2$$
$$n = -7$$
So,
$$\left(y^{2} - 2\right)^{2} - 7$$
Factorization
[src]
/ ____________\ / ____________\ / ___________\ / ___________\ | / ___ | | / ___ | | / ___ | | / ___ | \x + I*\/ -2 + \/ 7 /*\x - I*\/ -2 + \/ 7 /*\x + \/ 2 + \/ 7 /*\x - \/ 2 + \/ 7 /
$$\left(x - i \sqrt{-2 + \sqrt{7}}\right) \left(x + i \sqrt{-2 + \sqrt{7}}\right) \left(x + \sqrt{2 + \sqrt{7}}\right) \left(x - \sqrt{2 + \sqrt{7}}\right)$$
(((x + i*sqrt(-2 + sqrt(7)))*(x - i*sqrt(-2 + sqrt(7))))*(x + sqrt(2 + sqrt(7))))*(x - sqrt(2 + sqrt(7)))
Combining rational expressions
[src]
2 / 2\ -3 + y *\-4 + y /
$$y^{2} \left(y^{2} - 4\right) - 3$$
-3 + y^2*(-4 + y^2)