Mister Exam

# Factor -y^2+4*y-3 squared

An expression to simplify:

### The solution

You have entered [src]
   2
- y  + 4*y - 3
$$\left(- y^{2} + 4 y\right) - 3$$
-y^2 + 4*y - 3
Factorization [src]
(x - 1)*(x - 3)
$$\left(x - 3\right) \left(x - 1\right)$$
(x - 1)*(x - 3)
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
$$m = -2$$
$$n = 1$$
So,
$$1 - \left(y - 2\right)^{2}$$
General simplification [src]
      2
-3 - y  + 4*y
$$- y^{2} + 4 y - 3$$
-3 - y^2 + 4*y
-3.0 - y^2 + 4.0*y
-3.0 - y^2 + 4.0*y
Assemble expression [src]
      2
-3 - y  + 4*y
$$- y^{2} + 4 y - 3$$
-3 - y^2 + 4*y
Rational denominator [src]
      2
-3 - y  + 4*y
$$- y^{2} + 4 y - 3$$
-3 - y^2 + 4*y
Powers [src]
      2
-3 - y  + 4*y
$$- y^{2} + 4 y - 3$$
-3 - y^2 + 4*y
Common denominator [src]
      2
-3 - y  + 4*y
$$- y^{2} + 4 y - 3$$
-3 - y^2 + 4*y
Combinatorics [src]
-(-1 + y)*(-3 + y)
$$- \left(y - 3\right) \left(y - 1\right)$$
-(-1 + y)*(-3 + y)
Combining rational expressions [src]
-3 + y*(4 - y)
$$y \left(4 - y\right) - 3$$
-3 + y*(4 - y)
Trigonometric part [src]
      2
-3 - y  + 4*y
$$- y^{2} + 4 y - 3$$
-3 - y^2 + 4*y