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
$$4 a^{2} + \left(- a x + x^{2}\right) = \frac{15 x^{2}}{16} + \left(2 a - \frac{x}{4}\right)^{2}$$
/ / ____\\ / / ____\\
| 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]
$$4 a^{2} - a x + x^{2}$$
$$4 a^{2} - a x + x^{2}$$
Rational denominator
[src]
$$4 a^{2} - a x + x^{2}$$
$$4 a^{2} - a x + x^{2}$$
$$4 a^{2} - a x + x^{2}$$
Assemble expression
[src]
$$4 a^{2} - a x + x^{2}$$
Combining rational expressions
[src]
$$4 a^{2} + x \left(- a + x\right)$$
$$4 a^{2} - a x + x^{2}$$