Mister Exam
Factor -y^2-2*y+9 squared
The solution
Factorization
[src]
/ ____\ / ____\ \x + 1 - \/ 10 /*\x + 1 + \/ 10 /
$$\left(x + \left(1 - \sqrt{10}\right)\right) \left(x + \left(1 + \sqrt{10}\right)\right)$$
(x + 1 - sqrt(10))*(x + 1 + sqrt(10))
The perfect square
Let's highlight the perfect square of the square three-member
$$\left(- y^{2} - 2 y\right) + 9$$
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
$$a = -1$$
$$b = -2$$
$$c = 9$$
Then
$$m = 1$$
$$n = 10$$
So,
$$10 - \left(y + 1\right)^{2}$$
$$\left(- y^{2} - 2 y\right) + 9$$
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
$$a = -1$$
$$b = -2$$
$$c = 9$$
Then
$$m = 1$$
$$n = 10$$
So,
$$10 - \left(y + 1\right)^{2}$$