Solve 7/3a-a^2-a-1/3a2a+2/5a-5a^2+a^3

$$\frac{ 7 }{ 3 } a- { a }^{ 2 } -a- \frac{ 1 }{ 3 } a2a+ \frac{ 2 }{ 5 } a-5 { a }^{ 2 } + { a }^{ 3 }$$

Evaluate

$$-\frac{aa_{2}}{3}+a^{3}-6a^{2}+\frac{26a}{15}$$

Solution Steps

Combine \frac{7}{3}a and -a to get \frac{4}{3}a.

$$\frac{4}{3}a-a^{2}-\frac{1}{3}a_{2}a+\frac{2}{5}a-5a^{2}+a^{3}$$

Combine \frac{4}{3}a and \frac{2}{5}a to get \frac{26}{15}a.

$$\frac{26}{15}a-a^{2}-\frac{1}{3}a_{2}a-5a^{2}+a^{3}$$

Combine -a^{2} and -5a^{2} to get -6a^{2}.

$$\frac{26}{15}a-6a^{2}-\frac{1}{3}a_{2}a+a^{3}$$

Factor

$$\frac{a\left(15a^{2}-90a-5a_{2}+26\right)}{15}$$

Solution Steps

Factor out \frac{1}{15}.

$$\frac{35a-15a^{2}-15a-5a_{2}a+6a-75a^{2}+15a^{3}}{15}$$

Consider 35a-15a^{2}-15a-5a_{2}a+6a-75a^{2}+15a^{3}. Factor out a.

$$a\left(26-90a-5a_{2}+15a^{2}\right)$$

Rewrite the complete factored expression.

$$\frac{a\left(15a^{2}-90a-5a_{2}+26\right)}{15}$$