Solve 196a^4b-4a^2b

$$196 a ^ { 4 } b - 4 a ^ { 2 } b$$

Factor

$$4b\left(7a-1\right)\left(7a+1\right)a^{2}$$

Solution Steps

Factor out 4.

$$4\left(49a^{4}b-a^{2}b\right)$$

Consider 49a^{4}b-a^{2}b. Factor out a^{2}b.

$$a^{2}b\left(49a^{2}-1\right)$$

Consider 49a^{2}-1. Rewrite 49a^{2}-1 as \left(7a\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).

$$\left(7a-1\right)\left(7a+1\right)$$

Rewrite the complete factored expression.

$$4a^{2}b\left(7a-1\right)\left(7a+1\right)$$

Evaluate

$$4ba^{2}\left(49a^{2}-1\right)$$