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Expression simplification/ Factor perfect squares/ x^4+2*x^2+1

Factor x^4+2*x^2+1 squared

An expression to simplify:

The solution

You have entered [src] 
 4      2    
x  + 2*x  + 1
$$\left(x^{4} + 2 x^{2}\right) + 1$$ 
x^4 + 2*x^2 + 1
The perfect square
Let's highlight the perfect square of the square three-member
$$\left(x^{4} + 2 x^{2}\right) + 1$$
To do this, let's use the formula
$$a x^{4} + b x^{2} + c = a \left(m + x^{2}\right)^{2} + n$$
where
$$m = \frac{b}{2 a}$$
$$n = \frac{4 a c - b^{2}}{4 a}$$
In this case
$$a = 1$$
$$b = 2$$
$$c = 1$$
Then
$$m = 1$$
$$n = 0$$
So,
$$\left(x^{2} + 1\right)^{2}$$
General simplification [src] 
     4      2
1 + x  + 2*x
$$x^{4} + 2 x^{2} + 1$$ 
1 + x^4 + 2*x^2
Factorization [src] 
(x + I)*(x - I)
$$\left(x - i\right) \left(x + i\right)$$ 
(x + i)*(x - i)
Combining rational expressions [src] 
     2 /     2\
1 + x *\2 + x /
$$x^{2} \left(x^{2} + 2\right) + 1$$ 
1 + x^2*(2 + x^2)
Numerical answer [src] 
1.0 + x^4 + 2.0*x^2
1.0 + x^4 + 2.0*x^2
Common denominator [src] 
     4      2
1 + x  + 2*x
$$x^{4} + 2 x^{2} + 1$$ 
1 + x^4 + 2*x^2
Trigonometric part [src] 
     4      2
1 + x  + 2*x
$$x^{4} + 2 x^{2} + 1$$ 
1 + x^4 + 2*x^2
Powers [src] 
     4      2
1 + x  + 2*x
$$x^{4} + 2 x^{2} + 1$$ 
1 + x^4 + 2*x^2
Rational denominator [src] 
     4      2
1 + x  + 2*x
$$x^{4} + 2 x^{2} + 1$$ 
1 + x^4 + 2*x^2
Assemble expression [src] 
     4      2
1 + x  + 2*x
$$x^{4} + 2 x^{2} + 1$$ 
1 + x^4 + 2*x^2
Combinatorics [src] 
        2
/     2\ 
\1 + x /
$$\left(x^{2} + 1\right)^{2}$$ 
(1 + x^2)^2
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