Solve f(u)=u^4/4+2u^3/3

$$f ( u ) = \frac { u ^ { 4 } } { 4 } + \frac { 2 u ^ { 3 } } { 3 }$$

Evaluate

$$\frac{u^{4}}{4}+\frac{2u^{3}}{3}$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 4 and 3 is 12. Multiply \frac{u^{4}}{4} times \frac{3}{3}. Multiply \frac{2u^{3}}{3} times \frac{4}{4}.

$$\frac{3u^{4}}{12}+\frac{4\times 2u^{3}}{12}$$

Since \frac{3u^{4}}{12} and \frac{4\times 2u^{3}}{12} have the same denominator, add them by adding their numerators.

$$\frac{3u^{4}+4\times 2u^{3}}{12}$$

Do the multiplications in 3u^{4}+4\times 2u^{3}.

$$\frac{3u^{4}+8u^{3}}{12}$$

Factor

$$\frac{\left(3u+8\right)u^{3}}{12}$$

Solution Steps

Factor out \frac{1}{12}.

$$\frac{3u^{4}+8u^{3}}{12}$$

Consider 3u^{4}+8u^{3}. Factor out u^{3}.

$$u^{3}\left(3u+8\right)$$

Rewrite the complete factored expression.

$$\frac{u^{3}\left(3u+8\right)}{12}$$