Solve (1/9a^{2}+1/3a^2)(3/4ab^2-5/3ab^2-frac{7}{12}ab^2)

$$( \frac { 1 } { 9 } a ^ { 2 } + \frac { 1 } { 3 } a ^ { 2 } ) ( \frac { 3 } { 4 } a b ^ { 2 } - \frac { 5 } { 3 } a b ^ { 2 } - \frac { 7 } { 12 } a b ^ { 2 } )$$

Evaluate

$$-\frac{2b^{2}a^{3}}{3}$$

Solution Steps

Combine \frac{1}{9}a^{2} and \frac{1}{3}a^{2} to get \frac{4}{9}a^{2}.

$$\frac{4}{9}a^{2}\left(\frac{3}{4}ab^{2}-\frac{5}{3}ab^{2}-\frac{7}{12}ab^{2}\right)$$

Combine \frac{3}{4}ab^{2} and -\frac{5}{3}ab^{2} to get -\frac{11}{12}ab^{2}.

$$\frac{4}{9}a^{2}\left(-\frac{11}{12}ab^{2}-\frac{7}{12}ab^{2}\right)$$

Combine -\frac{11}{12}ab^{2} and -\frac{7}{12}ab^{2} to get -\frac{3}{2}ab^{2}.

$$\frac{4}{9}a^{2}\left(-\frac{3}{2}\right)ab^{2}$$

Multiply \frac{4}{9} and -\frac{3}{2} to get -\frac{2}{3}.

$$-\frac{2}{3}a^{2}ab^{2}$$

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

$$-\frac{2}{3}a^{3}b^{2}$$

Expand

$$-\frac{2b^{2}a^{3}}{3}$$

Solution Steps

Combine \frac{1}{9}a^{2} and \frac{1}{3}a^{2} to get \frac{4}{9}a^{2}.

$$\frac{4}{9}a^{2}\left(\frac{3}{4}ab^{2}-\frac{5}{3}ab^{2}-\frac{7}{12}ab^{2}\right)$$

Combine \frac{3}{4}ab^{2} and -\frac{5}{3}ab^{2} to get -\frac{11}{12}ab^{2}.

$$\frac{4}{9}a^{2}\left(-\frac{11}{12}ab^{2}-\frac{7}{12}ab^{2}\right)$$

Combine -\frac{11}{12}ab^{2} and -\frac{7}{12}ab^{2} to get -\frac{3}{2}ab^{2}.

$$\frac{4}{9}a^{2}\left(-\frac{3}{2}\right)ab^{2}$$

Multiply \frac{4}{9} and -\frac{3}{2} to get -\frac{2}{3}.

$$-\frac{2}{3}a^{2}ab^{2}$$

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

$$-\frac{2}{3}a^{3}b^{2}$$