Solve -a^2b^2+16c^6

$$- a ^ { 2 } b ^ { 2 } + 16 c ^ { 6 }$$

Factor

$$\left(-ab-4c^{3}\right)\left(ab-4c^{3}\right)$$

Solution Steps

Rewrite -a^{2}b^{2}+16c^{6} as \left(4c^{3}\right)^{2}-\left(-ab\right)^{2}. The difference of squares can be factored using the rule: p^{2}-q^{2}=\left(p-q\right)\left(p+q\right).

$$\left(4c^{3}+ab\right)\left(4c^{3}-ab\right)$$

Reorder the terms.

$$\left(ab+4c^{3}\right)\left(-ab+4c^{3}\right)$$

Evaluate

$$16c^{6}-\left(ab\right)^{2}$$