Solve ax^3+bx^2-ax-b

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

Factor

$$\left(x-1\right)\left(x+1\right)\left(ax+b\right)$$

Solution Steps

Do the grouping ax^{3}+bx^{2}-ax-b=\left(ax^{3}+bx^{2}\right)+\left(-ax-b\right), and factor out x^{2} in the first and -1 in the second group.

$$x^{2}\left(ax+b\right)-\left(ax+b\right)$$

Factor out common term ax+b by using distributive property.

$$\left(ax+b\right)\left(x^{2}-1\right)$$

Consider x^{2}-1. Rewrite x^{2}-1 as x^{2}-1^{2}. The difference of squares can be factored using the rule: p^{2}-q^{2}=\left(p-q\right)\left(p+q\right).

$$\left(x-1\right)\left(x+1\right)$$

Rewrite the complete factored expression.

$$\left(x-1\right)\left(x+1\right)\left(ax+b\right)$$

Evaluate

$$\left(x^{2}-1\right)\left(ax+b\right)$$