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Expression simplification/ Factor perfect squares/ x^2-x*t+t^2

Factor x^2-x*t+t^2 squared

An expression to simplify:

The solution

You have entered [src] 
 2          2
x  - x*t + t
$$t^{2} + \left(- t x + x^{2}\right)$$ 
x^2 - x*t + t^2
General simplification [src] 
 2    2      
t  + x  - t*x
$$t^{2} - t x + x^{2}$$ 
t^2 + x^2 - t*x
The perfect square
Let's highlight the perfect square of the square three-member
$$t^{2} + \left(- t x + x^{2}\right)$$
Let us write down the identical expression
$$t^{2} + \left(- t x + x^{2}\right) = \frac{3 x^{2}}{4} + \left(t^{2} - t x + \frac{x^{2}}{4}\right)$$
or
$$t^{2} + \left(- t x + x^{2}\right) = \frac{3 x^{2}}{4} + \left(t - \frac{x}{2}\right)^{2}$$
Factorization [src] 
/      /        ___\\ /      /        ___\\
|    x*\1 - I*\/ 3 /| |    x*\1 + I*\/ 3 /|
|t - ---------------|*|t - ---------------|
\           2       / \           2       /
$$\left(t - \frac{x \left(1 - \sqrt{3} i\right)}{2}\right) \left(t - \frac{x \left(1 + \sqrt{3} i\right)}{2}\right)$$ 
(t - x*(1 - i*sqrt(3))/2)*(t - x*(1 + i*sqrt(3))/2)
Numerical answer [src] 
t^2 + x^2 - t*x
t^2 + x^2 - t*x
Combinatorics [src] 
 2    2      
t  + x  - t*x
$$t^{2} - t x + x^{2}$$ 
t^2 + x^2 - t*x
Assemble expression [src] 
 2    2      
t  + x  - t*x
$$t^{2} - t x + x^{2}$$ 
t^2 + x^2 - t*x
Trigonometric part [src] 
 2    2      
t  + x  - t*x
$$t^{2} - t x + x^{2}$$ 
t^2 + x^2 - t*x
Combining rational expressions [src] 
 2            
t  + x*(x - t)
$$t^{2} + x \left(- t + x\right)$$ 
t^2 + x*(x - t)
Rational denominator [src] 
 2    2      
t  + x  - t*x
$$t^{2} - t x + x^{2}$$ 
t^2 + x^2 - t*x
Powers [src] 
 2    2      
t  + x  - t*x
$$t^{2} - t x + x^{2}$$ 
t^2 + x^2 - t*x
Common denominator [src] 
 2    2      
t  + x  - t*x
$$t^{2} - t x + x^{2}$$ 
t^2 + x^2 - t*x
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