Solve a^4-4a^2-a^3x+4ax

$$a ^ { 4 } - 4 a ^ { 2 } - a ^ { 3 } x + 4 a x$$

Factor

$$a\left(a-2\right)\left(a+2\right)\left(a-x\right)$$

Solution Steps

Factor out a.

$$a\left(a^{3}-4a-a^{2}x+4x\right)$$

Consider a^{3}-4a-a^{2}x+4x. Do the grouping a^{3}-4a-a^{2}x+4x=\left(a^{3}-4a\right)+\left(-a^{2}x+4x\right), and factor out a in the first and -x in the second group.

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

Factor out common term a^{2}-4 by using distributive property.

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

Consider a^{2}-4. Rewrite a^{2}-4 as a^{2}-2^{2}. The difference of squares can be factored using the rule: p^{2}-q^{2}=\left(p-q\right)\left(p+q\right).

$$\left(a-2\right)\left(a+2\right)$$

Rewrite the complete factored expression.

$$a\left(-x+a\right)\left(a-2\right)\left(a+2\right)$$

Evaluate

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