Solve {l}{A^4+A^3x-A^2x}{-Ax^2}

$$\left. \begin{array} { l } { A ^ { 4 } + A ^ { 3 } x - A ^ { 2 } x } \\ { - A x ^ { 2 } } \end{array} \right.$$

Factor

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

Solution Steps

Factor out A.

$$A\left(A^{3}+A^{2}x-Ax-x^{2}\right)$$

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

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

Factor out common term x+A by using distributive property.

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

Rewrite the complete factored expression.

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

Evaluate

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