Solve {l}{ax^2+b-bx^2}{-a}

$$\left. \begin{array} { l } { a x ^ { 2 } + b - b x ^ { 2 } } \\ { - a } \end{array} \right.$$

Factor

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

Solution Steps

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

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

Factor out common term x^{2}-1 by using distributive property.

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

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.

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

Evaluate

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