Mister Exam

# Factor x^2-x*a+4*a^2 squared

An expression to simplify:

### The solution

You have entered [src]
 2            2
x  - x*a + 4*a 
$$4 a^{2} + \left(- a x + x^{2}\right)$$
x^2 - x*a + 4*a^2
The perfect square
Let's highlight the perfect square of the square three-member
$$4 a^{2} + \left(- a x + x^{2}\right)$$
Let us write down the identical expression
$$4 a^{2} + \left(- a x + x^{2}\right) = \frac{15 x^{2}}{16} + \left(4 a^{2} - a x + \frac{x^{2}}{16}\right)$$
or
$$4 a^{2} + \left(- a x + x^{2}\right) = \frac{15 x^{2}}{16} + \left(2 a - \frac{x}{4}\right)^{2}$$
Factorization [src]
/      /        ____\\ /      /        ____\\
|    x*\1 - I*\/ 15 /| |    x*\1 + I*\/ 15 /|
|a - ----------------|*|a - ----------------|
\           8        / \           8        /
$$\left(a - \frac{x \left(1 - \sqrt{15} i\right)}{8}\right) \left(a - \frac{x \left(1 + \sqrt{15} i\right)}{8}\right)$$
(a - x*(1 - i*sqrt(15))/8)*(a - x*(1 + i*sqrt(15))/8)
General simplification [src]
 2      2
x  + 4*a  - a*x
$$4 a^{2} - a x + x^{2}$$
x^2 + 4*a^2 - a*x
Numerical answer [src]
x^2 + 4.0*a^2 - a*x
x^2 + 4.0*a^2 - a*x
Common denominator [src]
 2      2
x  + 4*a  - a*x
$$4 a^{2} - a x + x^{2}$$
x^2 + 4*a^2 - a*x
Rational denominator [src]
 2      2
x  + 4*a  - a*x
$$4 a^{2} - a x + x^{2}$$
x^2 + 4*a^2 - a*x
Combinatorics [src]
 2      2
x  + 4*a  - a*x
$$4 a^{2} - a x + x^{2}$$
x^2 + 4*a^2 - a*x
Powers [src]
 2      2
x  + 4*a  - a*x
$$4 a^{2} - a x + x^{2}$$
x^2 + 4*a^2 - a*x
Assemble expression [src]
 2      2
x  + 4*a  - a*x
$$4 a^{2} - a x + x^{2}$$
x^2 + 4*a^2 - a*x
Combining rational expressions [src]
   2
4*a  + x*(x - a)
$$4 a^{2} + x \left(- a + x\right)$$
4*a^2 + x*(x - a)
Trigonometric part [src]
 2      2
x  + 4*a  - a*x
$$4 a^{2} - a x + x^{2}$$
x^2 + 4*a^2 - a*x
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