Solve {l}{(a+5)*(24/5a^2}{-16/5a-4)*1/2}{+10-1/2a*1frac{24}{5}a^2}{-frac{16}{5})}

$$\left. \begin{array} { l } { ( a + 5 ) \times ( \frac { 24 } { 5 } a ^ { 2 } } \\ { - \frac { 16 } { 5 } a - 4 ) \times \frac { 1 } { 2 } } \\ { + 10 - \frac { 1 } { 2 } a \times 1 \frac { 24 } { 5 } a ^ { 2 } } \\ { - \frac { 16 } { 5 } ) } \end{array} \right.$$

Evaluate

$$-\frac{a^{3}}{2}+\frac{52a^{2}}{5}-10a-\frac{16}{5}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 1 and 2 to get 3.

$$\left(a+5\right)\left(\frac{24}{5}a^{2}-\frac{16}{5}a-4\right)\times \frac{1}{2}+10-\frac{1}{2}a^{3}\times \frac{1\times 5+24}{5}-\frac{16}{5}$$

Use the distributive property to multiply a+5 by \frac{24}{5}a^{2}-\frac{16}{5}a-4 and combine like terms.

$$\left(\frac{24}{5}a^{3}+\frac{104}{5}a^{2}-20a-20\right)\times \frac{1}{2}+10-\frac{1}{2}a^{3}\times \frac{1\times 5+24}{5}-\frac{16}{5}$$

Use the distributive property to multiply \frac{24}{5}a^{3}+\frac{104}{5}a^{2}-20a-20 by \frac{1}{2}.

$$\frac{12}{5}a^{3}+\frac{52}{5}a^{2}-10a-10+10-\frac{1}{2}a^{3}\times \frac{1\times 5+24}{5}-\frac{16}{5}$$

Add -10 and 10 to get 0.

$$\frac{12}{5}a^{3}+\frac{52}{5}a^{2}-10a-\frac{1}{2}a^{3}\times \frac{1\times 5+24}{5}-\frac{16}{5}$$

Multiply 1 and 5 to get 5.

$$\frac{12}{5}a^{3}+\frac{52}{5}a^{2}-10a-\frac{1}{2}a^{3}\times \frac{5+24}{5}-\frac{16}{5}$$

Add 5 and 24 to get 29.

$$\frac{12}{5}a^{3}+\frac{52}{5}a^{2}-10a-\frac{1}{2}a^{3}\times \frac{29}{5}-\frac{16}{5}$$

Multiply \frac{1}{2} and \frac{29}{5} to get \frac{29}{10}.

$$\frac{12}{5}a^{3}+\frac{52}{5}a^{2}-10a-\frac{29}{10}a^{3}-\frac{16}{5}$$

Combine \frac{12}{5}a^{3} and -\frac{29}{10}a^{3} to get -\frac{1}{2}a^{3}.

$$-\frac{1}{2}a^{3}+\frac{52}{5}a^{2}-10a-\frac{16}{5}$$

Expand

$$-\frac{a^{3}}{2}+\frac{52a^{2}}{5}-10a-\frac{16}{5}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 1 and 2 to get 3.

$$\left(a+5\right)\left(\frac{24}{5}a^{2}-\frac{16}{5}a-4\right)\times \frac{1}{2}+10-\frac{1}{2}a^{3}\times \frac{1\times 5+24}{5}-\frac{16}{5}$$

Use the distributive property to multiply a+5 by \frac{24}{5}a^{2}-\frac{16}{5}a-4 and combine like terms.

$$\left(\frac{24}{5}a^{3}+\frac{104}{5}a^{2}-20a-20\right)\times \frac{1}{2}+10-\frac{1}{2}a^{3}\times \frac{1\times 5+24}{5}-\frac{16}{5}$$

Use the distributive property to multiply \frac{24}{5}a^{3}+\frac{104}{5}a^{2}-20a-20 by \frac{1}{2}.

$$\frac{12}{5}a^{3}+\frac{52}{5}a^{2}-10a-10+10-\frac{1}{2}a^{3}\times \frac{1\times 5+24}{5}-\frac{16}{5}$$

Add -10 and 10 to get 0.

$$\frac{12}{5}a^{3}+\frac{52}{5}a^{2}-10a-\frac{1}{2}a^{3}\times \frac{1\times 5+24}{5}-\frac{16}{5}$$

Multiply 1 and 5 to get 5.

$$\frac{12}{5}a^{3}+\frac{52}{5}a^{2}-10a-\frac{1}{2}a^{3}\times \frac{5+24}{5}-\frac{16}{5}$$

Add 5 and 24 to get 29.

$$\frac{12}{5}a^{3}+\frac{52}{5}a^{2}-10a-\frac{1}{2}a^{3}\times \frac{29}{5}-\frac{16}{5}$$

Multiply \frac{1}{2} and \frac{29}{5} to get \frac{29}{10}.

$$\frac{12}{5}a^{3}+\frac{52}{5}a^{2}-10a-\frac{29}{10}a^{3}-\frac{16}{5}$$

Combine \frac{12}{5}a^{3} and -\frac{29}{10}a^{3} to get -\frac{1}{2}a^{3}.

$$-\frac{1}{2}a^{3}+\frac{52}{5}a^{2}-10a-\frac{16}{5}$$