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Expression simplification/ Factor perfect squares/ y^4+8*y^2+6

Factor y^4+8*y^2+6 squared

An expression to simplify:

The solution

You have entered [src] 
 4      2    
y  + 8*y  + 6
$$\left(y^{4} + 8 y^{2}\right) + 6$$ 
y^4 + 8*y^2 + 6
The perfect square
Let's highlight the perfect square of the square three-member
$$\left(y^{4} + 8 y^{2}\right) + 6$$
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
$$a = 1$$
$$b = 8$$
$$c = 6$$
Then
$$m = 4$$
$$n = -10$$
So,
$$\left(y^{2} + 4\right)^{2} - 10$$
Factorization [src] 
/         ____________\ /         ____________\ /         ____________\ /         ____________\
|        /       ____ | |        /       ____ | |        /       ____ | |        /       ____ |
\x + I*\/  4 - \/ 10  /*\x - I*\/  4 - \/ 10  /*\x + I*\/  4 + \/ 10  /*\x - I*\/  4 + \/ 10  /
$$\left(x - i \sqrt{4 - \sqrt{10}}\right) \left(x + i \sqrt{4 - \sqrt{10}}\right) \left(x + i \sqrt{\sqrt{10} + 4}\right) \left(x - i \sqrt{\sqrt{10} + 4}\right)$$ 
(((x + i*sqrt(4 - sqrt(10)))*(x - i*sqrt(4 - sqrt(10))))*(x + i*sqrt(4 + sqrt(10))))*(x - i*sqrt(4 + sqrt(10)))
General simplification [src] 
     4      2
6 + y  + 8*y
$$y^{4} + 8 y^{2} + 6$$ 
6 + y^4 + 8*y^2
Numerical answer [src] 
6.0 + y^4 + 8.0*y^2
6.0 + y^4 + 8.0*y^2
Rational denominator [src] 
     4      2
6 + y  + 8*y
$$y^{4} + 8 y^{2} + 6$$ 
6 + y^4 + 8*y^2
Assemble expression [src] 
     4      2
6 + y  + 8*y
$$y^{4} + 8 y^{2} + 6$$ 
6 + y^4 + 8*y^2
Combinatorics [src] 
     4      2
6 + y  + 8*y
$$y^{4} + 8 y^{2} + 6$$ 
6 + y^4 + 8*y^2
Combining rational expressions [src] 
     2 /     2\
6 + y *\8 + y /
$$y^{2} \left(y^{2} + 8\right) + 6$$ 
6 + y^2*(8 + y^2)
Common denominator [src] 
     4      2
6 + y  + 8*y
$$y^{4} + 8 y^{2} + 6$$ 
6 + y^4 + 8*y^2
Powers [src] 
     4      2
6 + y  + 8*y
$$y^{4} + 8 y^{2} + 6$$ 
6 + y^4 + 8*y^2
Trigonometric part [src] 
     4      2
6 + y  + 8*y
$$y^{4} + 8 y^{2} + 6$$ 
6 + y^4 + 8*y^2
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