Solve 1/4x^2-25y^8z^12

$$\frac { 1 } { 4 } x ^ { 2 } - 25 y ^ { 8 } z ^ { 12 }$$

Factor

$$\frac{\left(x-10y^{4}z^{6}\right)\left(x+10y^{4}z^{6}\right)}{4}$$

Solution Steps

Factor out \frac{1}{4}.

$$\frac{x^{2}-100y^{8}z^{12}}{4}$$

Consider x^{2}-100y^{8}z^{12}. Rewrite x^{2}-100y^{8}z^{12} as x^{2}-\left(10y^{4}z^{6}\right)^{2}. The difference of squares can be factored using the rule: a^{2}-b^{2}=\left(a-b\right)\left(a+b\right).

$$\left(x-10y^{4}z^{6}\right)\left(x+10y^{4}z^{6}\right)$$

Rewrite the complete factored expression.

$$\frac{\left(x-10y^{4}z^{6}\right)\left(x+10y^{4}z^{6}\right)}{4}$$

Evaluate

$$-25y^{8}z^{12}+\frac{x^{2}}{4}$$