Solve 4a^4b^3-a^2b

$$4 a ^ { 4 } b ^ { 3 } - a ^ { 2 } b$$

Factor

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

Solution Steps

Factor out a^{2}b.

$$a^{2}b\left(4a^{2}b^{2}-1\right)$$

Consider 4a^{2}b^{2}-1. Rewrite 4a^{2}b^{2}-1 as \left(2ab\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).

$$\left(2ab-1\right)\left(2ab+1\right)$$

Rewrite the complete factored expression.

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

Evaluate

$$ba^{2}\left(4\left(ab\right)^{2}-1\right)$$