Solve x^2/2-x^6/3

$$\frac{ { x }^{ 2 } }{ 2 } - \frac{ { x }^{ 6 } }{ 3 }$$

Evaluate

$$-\frac{x^{6}}{3}+\frac{x^{2}}{2}$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 2 and 3 is 6. Multiply \frac{x^{2}}{2} times \frac{3}{3}. Multiply \frac{x^{6}}{3} times \frac{2}{2}.

$$\frac{3x^{2}}{6}-\frac{2x^{6}}{6}$$

Since \frac{3x^{2}}{6} and \frac{2x^{6}}{6} have the same denominator, subtract them by subtracting their numerators.

$$\frac{3x^{2}-2x^{6}}{6}$$

Factor

$$\frac{x^{2}\left(3-2x^{4}\right)}{6}$$

Solution Steps

Factor out \frac{1}{6}.

$$\frac{3x^{2}-2x^{6}}{6}$$

Consider 3x^{2}-2x^{6}. Factor out x^{2}.

$$x^{2}\left(3-2x^{4}\right)$$

Rewrite the complete factored expression. Polynomial 3-2x^{4} is not factored since it does not have any rational roots.

$$\frac{x^{2}\left(3-2x^{4}\right)}{6}$$