Solve x^3/8-27

$$\frac { x ^ { 3 } } { 8 } - 27$$

Factor

$$\frac{\left(x-6\right)\left(x^{2}+6x+36\right)}{8}$$

Solution Steps

Factor out \frac{1}{8}.

$$\frac{x^{3}-216}{8}$$

Consider x^{3}-216. Rewrite x^{3}-216 as x^{3}-6^{3}. The difference of cubes can be factored using the rule: a^{3}-b^{3}=\left(a-b\right)\left(a^{2}+ab+b^{2}\right).

$$\left(x-6\right)\left(x^{2}+6x+36\right)$$

Rewrite the complete factored expression. Polynomial x^{2}+6x+36 is not factored since it does not have any rational roots.

$$\frac{\left(x-6\right)\left(x^{2}+6x+36\right)}{8}$$

Evaluate

$$\frac{x^{3}}{8}-27$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Multiply 27 times \frac{8}{8}.

$$\frac{x^{3}}{8}-\frac{27\times 8}{8}$$

Since \frac{x^{3}}{8} and \frac{27\times 8}{8} have the same denominator, subtract them by subtracting their numerators.

$$\frac{x^{3}-27\times 8}{8}$$

Do the multiplications in x^{3}-27\times 8.

$$\frac{x^{3}-216}{8}$$