Solve a^5-a^3b^2

$$a ^ { 5 } - a ^ { 3 } b ^ { 2 }$$

Factor

$$\left(a-b\right)\left(a+b\right)a^{3}$$

Solution Steps

Factor out a^{3}.

$$a^{3}\left(a^{2}-b^{2}\right)$$

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

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

Rewrite the complete factored expression.

$$a^{3}\left(a-b\right)\left(a+b\right)$$

Evaluate

$$\left(a^{2}-b^{2}\right)a^{3}$$