Solve [9/5a^{2}c-a^{2}c)*(c^{3}-1/3c^{3}-1/6c^3)*(4/5ab^2-frac{1}{6}ab^2+frac{1}{5}ab^2)

$$[ \frac { 9 } { 5 } a ^ { 2 } c - a ^ { 2 } c ) \cdot ( c ^ { 3 } - \frac { 1 } { 3 } c ^ { 3 } - \frac { 1 } { 6 } c ^ { 3 } ) \cdot ( \frac { 4 } { 5 } a b ^ { 2 } - \frac { 1 } { 6 } a b ^ { 2 } + \frac { 1 } { 5 } a b ^ { 2 } )$$

Evaluate

$$\frac{b^{2}a^{3}c^{4}}{3}$$

Solution Steps

Combine \frac{9}{5}a^{2}c and -a^{2}c to get \frac{4}{5}a^{2}c.

$$\frac{4}{5}a^{2}c\left(c^{3}-\frac{1}{3}c^{3}-\frac{1}{6}c^{3}\right)\left(\frac{4}{5}ab^{2}-\frac{1}{6}ab^{2}+\frac{1}{5}ab^{2}\right)$$

Combine c^{3} and -\frac{1}{3}c^{3} to get \frac{2}{3}c^{3}.

$$\frac{4}{5}a^{2}c\left(\frac{2}{3}c^{3}-\frac{1}{6}c^{3}\right)\left(\frac{4}{5}ab^{2}-\frac{1}{6}ab^{2}+\frac{1}{5}ab^{2}\right)$$

Combine \frac{2}{3}c^{3} and -\frac{1}{6}c^{3} to get \frac{1}{2}c^{3}.

$$\frac{4}{5}a^{2}c\times \frac{1}{2}c^{3}\left(\frac{4}{5}ab^{2}-\frac{1}{6}ab^{2}+\frac{1}{5}ab^{2}\right)$$

Multiply \frac{4}{5} and \frac{1}{2} to get \frac{2}{5}.

$$\frac{2}{5}a^{2}cc^{3}\left(\frac{4}{5}ab^{2}-\frac{1}{6}ab^{2}+\frac{1}{5}ab^{2}\right)$$

To multiply powers of the same base, add their exponents. Add 1 and 3 to get 4.

$$\frac{2}{5}a^{2}c^{4}\left(\frac{4}{5}ab^{2}-\frac{1}{6}ab^{2}+\frac{1}{5}ab^{2}\right)$$

Combine \frac{4}{5}ab^{2} and -\frac{1}{6}ab^{2} to get \frac{19}{30}ab^{2}.

$$\frac{2}{5}a^{2}c^{4}\left(\frac{19}{30}ab^{2}+\frac{1}{5}ab^{2}\right)$$

Combine \frac{19}{30}ab^{2} and \frac{1}{5}ab^{2} to get \frac{5}{6}ab^{2}.

$$\frac{2}{5}a^{2}c^{4}\times \frac{5}{6}ab^{2}$$

Multiply \frac{2}{5} and \frac{5}{6} to get \frac{1}{3}.

$$\frac{1}{3}a^{2}c^{4}ab^{2}$$

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

$$\frac{1}{3}a^{3}c^{4}b^{2}$$

Expand

$$\frac{b^{2}a^{3}c^{4}}{3}$$

Solution Steps

Combine \frac{9}{5}a^{2}c and -a^{2}c to get \frac{4}{5}a^{2}c.

$$\frac{4}{5}a^{2}c\left(c^{3}-\frac{1}{3}c^{3}-\frac{1}{6}c^{3}\right)\left(\frac{4}{5}ab^{2}-\frac{1}{6}ab^{2}+\frac{1}{5}ab^{2}\right)$$

Combine c^{3} and -\frac{1}{3}c^{3} to get \frac{2}{3}c^{3}.

$$\frac{4}{5}a^{2}c\left(\frac{2}{3}c^{3}-\frac{1}{6}c^{3}\right)\left(\frac{4}{5}ab^{2}-\frac{1}{6}ab^{2}+\frac{1}{5}ab^{2}\right)$$

Combine \frac{2}{3}c^{3} and -\frac{1}{6}c^{3} to get \frac{1}{2}c^{3}.

$$\frac{4}{5}a^{2}c\times \frac{1}{2}c^{3}\left(\frac{4}{5}ab^{2}-\frac{1}{6}ab^{2}+\frac{1}{5}ab^{2}\right)$$

Multiply \frac{4}{5} and \frac{1}{2} to get \frac{2}{5}.

$$\frac{2}{5}a^{2}cc^{3}\left(\frac{4}{5}ab^{2}-\frac{1}{6}ab^{2}+\frac{1}{5}ab^{2}\right)$$

To multiply powers of the same base, add their exponents. Add 1 and 3 to get 4.

$$\frac{2}{5}a^{2}c^{4}\left(\frac{4}{5}ab^{2}-\frac{1}{6}ab^{2}+\frac{1}{5}ab^{2}\right)$$

Combine \frac{4}{5}ab^{2} and -\frac{1}{6}ab^{2} to get \frac{19}{30}ab^{2}.

$$\frac{2}{5}a^{2}c^{4}\left(\frac{19}{30}ab^{2}+\frac{1}{5}ab^{2}\right)$$

Combine \frac{19}{30}ab^{2} and \frac{1}{5}ab^{2} to get \frac{5}{6}ab^{2}.

$$\frac{2}{5}a^{2}c^{4}\times \frac{5}{6}ab^{2}$$

Multiply \frac{2}{5} and \frac{5}{6} to get \frac{1}{3}.

$$\frac{1}{3}a^{2}c^{4}ab^{2}$$

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

$$\frac{1}{3}a^{3}c^{4}b^{2}$$