Solve x^12y^4z^8-289

$$x ^ { 12 } y ^ { 4 } z ^ { 8 } - 289$$

Factor

$$\left(y^{2}z^{4}x^{6}-17\right)\left(y^{2}z^{4}x^{6}+17\right)$$

Solution Steps

Rewrite x^{12}y^{4}z^{8}-289 as \left(x^{6}y^{2}z^{4}\right)^{2}-17^{2}. The difference of squares can be factored using the rule: a^{2}-b^{2}=\left(a-b\right)\left(a+b\right).

$$\left(x^{6}y^{2}z^{4}-17\right)\left(x^{6}y^{2}z^{4}+17\right)$$

Reorder the terms.

$$\left(y^{2}z^{4}x^{6}-17\right)\left(y^{2}z^{4}x^{6}+17\right)$$

Evaluate

$$y^{4}z^{8}x^{12}-289$$