Mister Exam
Factor -4*y^2-6*y+12 squared
The solution
The perfect square
Let's highlight the perfect square of the square three-member
$$\left(- 4 y^{2} - 6 y\right) + 12$$
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
$$a = -4$$
$$b = -6$$
$$c = 12$$
Then
$$m = \frac{3}{4}$$
$$n = \frac{57}{4}$$
So,
$$\frac{57}{4} - 4 \left(y + \frac{3}{4}\right)^{2}$$
$$\left(- 4 y^{2} - 6 y\right) + 12$$
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
$$a = -4$$
$$b = -6$$
$$c = 12$$
Then
$$m = \frac{3}{4}$$
$$n = \frac{57}{4}$$
So,
$$\frac{57}{4} - 4 \left(y + \frac{3}{4}\right)^{2}$$
Factorization
[src]
/ ____\ / ____\ | 3 \/ 57 | | 3 \/ 57 | |x + - - ------|*|x + - + ------| \ 4 4 / \ 4 4 /
$$\left(x + \left(\frac{3}{4} - \frac{\sqrt{57}}{4}\right)\right) \left(x + \left(\frac{3}{4} + \frac{\sqrt{57}}{4}\right)\right)$$
(x + 3/4 - sqrt(57)/4)*(x + 3/4 + sqrt(57)/4)
Combining rational expressions
[src]
2*(6 + y*(-3 - 2*y))
$$2 \left(y \left(- 2 y - 3\right) + 6\right)$$
2*(6 + y*(-3 - 2*y))