Mister Exam
Factor y^4-8*y^2-2 squared
The solution
The perfect square
Let's highlight the perfect square of the square three-member
$$\left(y^{4} - 8 y^{2}\right) - 2$$
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
$$a = 1$$
$$b = -8$$
$$c = -2$$
Then
$$m = -4$$
$$n = -18$$
So,
$$\left(y^{2} - 4\right)^{2} - 18$$
$$\left(y^{4} - 8 y^{2}\right) - 2$$
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
$$a = 1$$
$$b = -8$$
$$c = -2$$
Then
$$m = -4$$
$$n = -18$$
So,
$$\left(y^{2} - 4\right)^{2} - 18$$
Factorization
[src]
/ ______________\ / ______________\ / _____________\ / _____________\ | / ___ | | / ___ | | / ___ | | / ___ | \x + I*\/ -4 + 3*\/ 2 /*\x - I*\/ -4 + 3*\/ 2 /*\x + \/ 4 + 3*\/ 2 /*\x - \/ 4 + 3*\/ 2 /
$$\left(x - i \sqrt{-4 + 3 \sqrt{2}}\right) \left(x + i \sqrt{-4 + 3 \sqrt{2}}\right) \left(x + \sqrt{4 + 3 \sqrt{2}}\right) \left(x - \sqrt{4 + 3 \sqrt{2}}\right)$$
(((x + i*sqrt(-4 + 3*sqrt(2)))*(x - i*sqrt(-4 + 3*sqrt(2))))*(x + sqrt(4 + 3*sqrt(2))))*(x - sqrt(4 + 3*sqrt(2)))
Combining rational expressions
[src]
2 / 2\ -2 + y *\-8 + y /
$$y^{2} \left(y^{2} - 8\right) - 2$$
-2 + y^2*(-8 + y^2)