Mister Exam

# Factor -y^4-14*y^2-2 squared

An expression to simplify:

### The solution

You have entered [src]
   4       2
- y  - 14*y  - 2
$$\left(- y^{4} - 14 y^{2}\right) - 2$$
-y^4 - 14*y^2 - 2
General simplification [src]
      4       2
-2 - y  - 14*y 
$$- y^{4} - 14 y^{2} - 2$$
-2 - y^4 - 14*y^2
Factorization [src]
/         ____________\ /         ____________\ /         ____________\ /         ____________\
|        /       ____ | |        /       ____ | |        /       ____ | |        /       ____ |
\x + I*\/  7 - \/ 47  /*\x - I*\/  7 - \/ 47  /*\x + I*\/  7 + \/ 47  /*\x - I*\/  7 + \/ 47  /
$$\left(x - i \sqrt{7 - \sqrt{47}}\right) \left(x + i \sqrt{7 - \sqrt{47}}\right) \left(x + i \sqrt{\sqrt{47} + 7}\right) \left(x - i \sqrt{\sqrt{47} + 7}\right)$$
(((x + i*sqrt(7 - sqrt(47)))*(x - i*sqrt(7 - sqrt(47))))*(x + i*sqrt(7 + sqrt(47))))*(x - i*sqrt(7 + sqrt(47)))
The perfect square
Let's highlight the perfect square of the square three-member
$$\left(- y^{4} - 14 y^{2}\right) - 2$$
To do this, let's use the formula
$$a y^{4} + b y^{2} + c = a \left(m + y^{2}\right)^{2} + n$$
where
$$m = \frac{b}{2 a}$$
$$n = \frac{4 a c - b^{2}}{4 a}$$
In this case
$$a = -1$$
$$b = -14$$
$$c = -2$$
Then
$$m = 7$$
$$n = 47$$
So,
$$47 - \left(y^{2} + 7\right)^{2}$$
-2.0 - y^4 - 14.0*y^2
-2.0 - y^4 - 14.0*y^2
Common denominator [src]
      4       2
-2 - y  - 14*y 
$$- y^{4} - 14 y^{2} - 2$$
-2 - y^4 - 14*y^2
Powers [src]
      4       2
-2 - y  - 14*y 
$$- y^{4} - 14 y^{2} - 2$$
-2 - y^4 - 14*y^2
Trigonometric part [src]
      4       2
-2 - y  - 14*y 
$$- y^{4} - 14 y^{2} - 2$$
-2 - y^4 - 14*y^2
Rational denominator [src]
      4       2
-2 - y  - 14*y 
$$- y^{4} - 14 y^{2} - 2$$
-2 - y^4 - 14*y^2
Combinatorics [src]
      4       2
-2 - y  - 14*y 
$$- y^{4} - 14 y^{2} - 2$$
-2 - y^4 - 14*y^2
Assemble expression [src]
      4       2
-2 - y  - 14*y 
$$- y^{4} - 14 y^{2} - 2$$
-2 - y^4 - 14*y^2
Combining rational expressions [src]
      2 /       2\
-2 + y *\-14 - y /
$$y^{2} \left(- y^{2} - 14\right) - 2$$
-2 + y^2*(-14 - y^2)