Mister Exam
Factor y^2-4*y-3 squared
The solution
Factorization
[src]
/ ___\ / ___\ \x + -2 + \/ 7 /*\x + -2 - \/ 7 /
$$\left(x + \left(-2 + \sqrt{7}\right)\right) \left(x + \left(- \sqrt{7} - 2\right)\right)$$
(x - 2 + sqrt(7))*(x - 2 - sqrt(7))
The perfect square
Let's highlight the perfect square of the square three-member
$$\left(y^{2} - 4 y\right) - 3$$
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
$$a = 1$$
$$b = -4$$
$$c = -3$$
Then
$$m = -2$$
$$n = -7$$
So,
$$\left(y - 2\right)^{2} - 7$$
$$\left(y^{2} - 4 y\right) - 3$$
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
$$a = 1$$
$$b = -4$$
$$c = -3$$
Then
$$m = -2$$
$$n = -7$$
So,
$$\left(y - 2\right)^{2} - 7$$