Solve a^3/6+left(a+2right)left(a-1right)^2/6

$$\frac{ { a }^{ 3 } }{ 6 } + \frac{ \left( a+2 \right) { \left( a-1 \right) }^{ 2 } }{ 6 }$$

Evaluate

$$\frac{a^{3}}{3}-\frac{a}{2}+\frac{1}{3}$$

Short Solution Steps

Since \frac{a^{3}}{6} and \frac{\left(a+2\right)\left(a-1\right)^{2}}{6} have the same denominator, add them by adding their numerators.

$$\frac{a^{3}+\left(a+2\right)\left(a-1\right)^{2}}{6}$$

Do the multiplications in a^{3}+\left(a+2\right)\left(a-1\right)^{2}.

$$\frac{a^{3}+a^{3}-2a^{2}+a+2a^{2}-4a+2}{6}$$

Combine like terms in a^{3}+a^{3}-2a^{2}+a+2a^{2}-4a+2.

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

Expand

$$\frac{a^{3}}{3}-\frac{a}{2}+\frac{1}{3}$$

Short Solution Steps

Since \frac{a^{3}}{6} and \frac{\left(a+2\right)\left(a-1\right)^{2}}{6} have the same denominator, add them by adding their numerators.

$$\frac{a^{3}+\left(a+2\right)\left(a-1\right)^{2}}{6}$$

Do the multiplications in a^{3}+\left(a+2\right)\left(a-1\right)^{2}.

$$\frac{a^{3}+a^{3}-2a^{2}+a+2a^{2}-4a+2}{6}$$

Combine like terms in a^{3}+a^{3}-2a^{2}+a+2a^{2}-4a+2.

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