Solve 12a^5b^3-147a^3b

$$12 a ^ { 5 } b ^ { 3 } - 147 a ^ { 3 } b$$

Factor

$$3b\left(2ab-7\right)\left(2ab+7\right)a^{3}$$

Solution Steps

Factor out 3.

$$3\left(4a^{5}b^{3}-49a^{3}b\right)$$

Consider 4a^{5}b^{3}-49a^{3}b. Factor out a^{3}b.

$$a^{3}b\left(4a^{2}b^{2}-49\right)$$

Consider 4a^{2}b^{2}-49. Rewrite 4a^{2}b^{2}-49 as \left(2ab\right)^{2}-7^{2}. The difference of squares can be factored using the rule: p^{2}-q^{2}=\left(p-q\right)\left(p+q\right).

$$\left(2ab-7\right)\left(2ab+7\right)$$

Rewrite the complete factored expression.

$$3a^{3}b\left(2ab-7\right)\left(2ab+7\right)$$

Evaluate

$$3ba^{3}\left(4\left(ab\right)^{2}-49\right)$$