Solve 128a^4-16ab^3

$$128 { a }^{ 4 } -16a { b }^{ 3 }$$

Factor

$$16a\left(2a-b\right)\left(4a^{2}+2ab+b^{2}\right)$$

Solution Steps

Factor out 16.

$$16\left(8a^{4}-ab^{3}\right)$$

Consider 8a^{4}-ab^{3}. Factor out a.

$$a\left(8a^{3}-b^{3}\right)$$

Consider 8a^{3}-b^{3}. Rewrite 8a^{3}-b^{3} as \left(2a\right)^{3}-b^{3}. The difference of cubes can be factored using the rule: p^{3}-q^{3}=\left(p-q\right)\left(p^{2}+pq+q^{2}\right).

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

Rewrite the complete factored expression.

$$16a\left(2a-b\right)\left(4a^{2}+2ab+b^{2}\right)$$

Evaluate

$$128a^{4}-16ab^{3}$$