Solve 196-n^6p^4q^2

$$196 - n ^ { 6 } p ^ { 4 } q ^ { 2 }$$

Factor

$$\left(-qp^{2}n^{3}-14\right)\left(qp^{2}n^{3}-14\right)$$

Solution Steps

Rewrite 196-n^{6}p^{4}q^{2} as 14^{2}-\left(-n^{3}p^{2}q\right)^{2}. The difference of squares can be factored using the rule: a^{2}-b^{2}=\left(a-b\right)\left(a+b\right).

$$\left(14+n^{3}p^{2}q\right)\left(14-n^{3}p^{2}q\right)$$

Reorder the terms.

$$\left(qp^{2}n^{3}+14\right)\left(-qp^{2}n^{3}+14\right)$$

Evaluate

$$196-q^{2}p^{4}n^{6}$$