Solve 25a^5b^3-a^3b

$$25 a ^ { 5 } b ^ { 3 } - a ^ { 3 } b$$

Factor

$$b\left(5ab-1\right)\left(5ab+1\right)a^{3}$$

Solution Steps

Factor out a^{3}b.

$$a^{3}b\left(25a^{2}b^{2}-1\right)$$

Consider 25a^{2}b^{2}-1. Rewrite 25a^{2}b^{2}-1 as \left(5ab\right)^{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).

$$\left(5ab-1\right)\left(5ab+1\right)$$

Rewrite the complete factored expression.

$$a^{3}b\left(5ab-1\right)\left(5ab+1\right)$$

Evaluate

$$ba^{3}\left(25\left(ab\right)^{2}-1\right)$$