Solve a^2-2ax+x^2+4a-4x

$$a ^ { 2 } - 2 a x + x ^ { 2 } + 4 a - 4 x$$

Factor

$$\left(a-x\right)\left(4+a-x\right)$$

Solution Steps

Consider a^{2}-2ax+x^{2}+4a-4x as a polynomial over variable a.

$$a^{2}+\left(-2x+4\right)a+x^{2}-4x$$

Find one factor of the form a^{k}+m, where a^{k} divides the monomial with the highest power a^{2} and m divides the constant factor x^{2}-4x. One such factor is -x+a. Factor the polynomial by dividing it by this factor.

$$\left(-x+a\right)\left(-x+a+4\right)$$

Evaluate

$$\left(a-x\right)\left(4+a-x\right)$$