Mister Exam
Factor -y^4+4*y^2+8 squared
The solution
The perfect square
Let's highlight the perfect square of the square three-member
$$\left(- y^{4} + 4 y^{2}\right) + 8$$
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
$$a = -1$$
$$b = 4$$
$$c = 8$$
Then
$$m = -2$$
$$n = 12$$
So,
$$12 - \left(y^{2} - 2\right)^{2}$$
$$\left(- y^{4} + 4 y^{2}\right) + 8$$
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
$$a = -1$$
$$b = 4$$
$$c = 8$$
Then
$$m = -2$$
$$n = 12$$
So,
$$12 - \left(y^{2} - 2\right)^{2}$$
Factorization
[src]
/ ______________\ / ______________\ / _____________\ / _____________\ | / ___ | | / ___ | | / ___ | | / ___ | \x + I*\/ -2 + 2*\/ 3 /*\x - I*\/ -2 + 2*\/ 3 /*\x + \/ 2 + 2*\/ 3 /*\x - \/ 2 + 2*\/ 3 /
$$\left(x - i \sqrt{-2 + 2 \sqrt{3}}\right) \left(x + i \sqrt{-2 + 2 \sqrt{3}}\right) \left(x + \sqrt{2 + 2 \sqrt{3}}\right) \left(x - \sqrt{2 + 2 \sqrt{3}}\right)$$
(((x + i*sqrt(-2 + 2*sqrt(3)))*(x - i*sqrt(-2 + 2*sqrt(3))))*(x + sqrt(2 + 2*sqrt(3))))*(x - sqrt(2 + 2*sqrt(3)))
Combining rational expressions
[src]
2 / 2\ 8 + y *\4 - y /
$$y^{2} \left(4 - y^{2}\right) + 8$$
8 + y^2*(4 - y^2)