Solve p^3+1/p^3+26/27

$$p ^ { 3 } + \frac { 1 } { p ^ { 3 } } + \frac { 26 } { 27 }$$

Evaluate

$$p^{3}+\frac{26}{27}+\frac{1}{p^{3}}$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of p^{3} and 27 is 27p^{3}. Multiply \frac{1}{p^{3}} times \frac{27}{27}. Multiply \frac{26}{27} times \frac{p^{3}}{p^{3}}.

$$p^{3}+\frac{27}{27p^{3}}+\frac{26p^{3}}{27p^{3}}$$

Since \frac{27}{27p^{3}} and \frac{26p^{3}}{27p^{3}} have the same denominator, add them by adding their numerators.

$$p^{3}+\frac{27+26p^{3}}{27p^{3}}$$

To add or subtract expressions, expand them to make their denominators the same. Multiply p^{3} times \frac{27p^{3}}{27p^{3}}.

$$\frac{p^{3}\times 27p^{3}}{27p^{3}}+\frac{27+26p^{3}}{27p^{3}}$$

Since \frac{p^{3}\times 27p^{3}}{27p^{3}} and \frac{27+26p^{3}}{27p^{3}} have the same denominator, add them by adding their numerators.

$$\frac{p^{3}\times 27p^{3}+27+26p^{3}}{27p^{3}}$$

Do the multiplications in p^{3}\times 27p^{3}+27+26p^{3}.

$$\frac{27p^{6}+27+26p^{3}}{27p^{3}}$$

Factor

$$\frac{\left(3p^{2}-p+3\right)\left(9p^{4}+3p^{3}-8p^{2}+3p+9\right)}{27p^{3}}$$