Mister Exam
Factor -y^4-8*y^2+7 squared
The solution
The perfect square
Let's highlight the perfect square of the square three-member
$$\left(- y^{4} - 8 y^{2}\right) + 7$$
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
$$a = -1$$
$$b = -8$$
$$c = 7$$
Then
$$m = 4$$
$$n = 23$$
So,
$$23 - \left(y^{2} + 4\right)^{2}$$
$$\left(- y^{4} - 8 y^{2}\right) + 7$$
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
$$a = -1$$
$$b = -8$$
$$c = 7$$
Then
$$m = 4$$
$$n = 23$$
So,
$$23 - \left(y^{2} + 4\right)^{2}$$
Factorization
[src]
/ ____________\ / ____________\ / _____________\ / _____________\ | / ____ | | / ____ | | / ____ | | / ____ | \x + I*\/ 4 + \/ 23 /*\x - I*\/ 4 + \/ 23 /*\x + \/ -4 + \/ 23 /*\x - \/ -4 + \/ 23 /
$$\left(x - i \sqrt{4 + \sqrt{23}}\right) \left(x + i \sqrt{4 + \sqrt{23}}\right) \left(x + \sqrt{-4 + \sqrt{23}}\right) \left(x - \sqrt{-4 + \sqrt{23}}\right)$$
(((x + i*sqrt(4 + sqrt(23)))*(x - i*sqrt(4 + sqrt(23))))*(x + sqrt(-4 + sqrt(23))))*(x - sqrt(-4 + sqrt(23)))
Combining rational expressions
[src]
2 / 2\ 7 + y *\-8 - y /
$$y^{2} \left(- y^{2} - 8\right) + 7$$
7 + y^2*(-8 - y^2)