Mister Exam
Factor -2*y^2+4*y-3 squared
The solution
Factorization
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/ ___\ / ___\ | I*\/ 2 | | I*\/ 2 | |x + -1 + -------|*|x + -1 - -------| \ 2 / \ 2 /
$$\left(x + \left(-1 - \frac{\sqrt{2} i}{2}\right)\right) \left(x + \left(-1 + \frac{\sqrt{2} i}{2}\right)\right)$$
(x - 1 + i*sqrt(2)/2)*(x - 1 - i*sqrt(2)/2)
The perfect square
Let's highlight the perfect square of the square three-member
$$\left(- 2 y^{2} + 4 y\right) - 3$$
To do this, let's use the formula
$$a y^{2} + b y + c = a \left(m + y\right)^{2} + n$$
where
$$m = \frac{b}{2 a}$$
$$n = \frac{4 a c - b^{2}}{4 a}$$
In this case
$$a = -2$$
$$b = 4$$
$$c = -3$$
Then
$$m = -1$$
$$n = -1$$
So,
$$- 2 \left(y - 1\right)^{2} - 1$$
$$\left(- 2 y^{2} + 4 y\right) - 3$$
To do this, let's use the formula
$$a y^{2} + b y + c = a \left(m + y\right)^{2} + n$$
where
$$m = \frac{b}{2 a}$$
$$n = \frac{4 a c - b^{2}}{4 a}$$
In this case
$$a = -2$$
$$b = 4$$
$$c = -3$$
Then
$$m = -1$$
$$n = -1$$
So,
$$- 2 \left(y - 1\right)^{2} - 1$$
Combining rational expressions
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-3 + 2*y*(2 - y)
$$2 y \left(2 - y\right) - 3$$
-3 + 2*y*(2 - y)