Solve (5/2a^2b-99/46a^2b)(7/6b^2c-7/12b^2c)(frac{5}{6}c-frac{2}{7}c)

$$( \frac { 5 } { 2 } a ^ { 2 } b - \frac { 99 } { 46 } a ^ { 2 } b ) ( \frac { 7 } { 6 } b ^ { 2 } c - \frac { 7 } { 12 } b ^ { 2 } c ) ( \frac { 5 } { 6 } c - \frac { 2 } { 7 } c )$$

Evaluate

$$\frac{b^{3}\left(ac\right)^{2}}{9}$$

Solution Steps

Combine \frac{5}{2}a^{2}b and -\frac{99}{46}a^{2}b to get \frac{8}{23}a^{2}b.

$$\frac{8}{23}a^{2}b\left(\frac{7}{6}b^{2}c-\frac{7}{12}b^{2}c\right)\left(\frac{5}{6}c-\frac{2}{7}c\right)$$

Combine \frac{7}{6}b^{2}c and -\frac{7}{12}b^{2}c to get \frac{7}{12}b^{2}c.

$$\frac{8}{23}a^{2}b\times \frac{7}{12}b^{2}c\left(\frac{5}{6}c-\frac{2}{7}c\right)$$

Multiply \frac{8}{23} and \frac{7}{12} to get \frac{14}{69}.

$$\frac{14}{69}a^{2}bb^{2}c\left(\frac{5}{6}c-\frac{2}{7}c\right)$$

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

$$\frac{14}{69}a^{2}b^{3}c\left(\frac{5}{6}c-\frac{2}{7}c\right)$$

Combine \frac{5}{6}c and -\frac{2}{7}c to get \frac{23}{42}c.

$$\frac{14}{69}a^{2}b^{3}c\times \frac{23}{42}c$$

Multiply \frac{14}{69} and \frac{23}{42} to get \frac{1}{9}.

$$\frac{1}{9}a^{2}b^{3}cc$$

Multiply c and c to get c^{2}.

$$\frac{1}{9}a^{2}b^{3}c^{2}$$

Expand

$$\frac{b^{3}\left(ac\right)^{2}}{9}$$

Solution Steps

Combine \frac{5}{2}a^{2}b and -\frac{99}{46}a^{2}b to get \frac{8}{23}a^{2}b.

$$\frac{8}{23}a^{2}b\left(\frac{7}{6}b^{2}c-\frac{7}{12}b^{2}c\right)\left(\frac{5}{6}c-\frac{2}{7}c\right)$$

Combine \frac{7}{6}b^{2}c and -\frac{7}{12}b^{2}c to get \frac{7}{12}b^{2}c.

$$\frac{8}{23}a^{2}b\times \frac{7}{12}b^{2}c\left(\frac{5}{6}c-\frac{2}{7}c\right)$$

Multiply \frac{8}{23} and \frac{7}{12} to get \frac{14}{69}.

$$\frac{14}{69}a^{2}bb^{2}c\left(\frac{5}{6}c-\frac{2}{7}c\right)$$

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

$$\frac{14}{69}a^{2}b^{3}c\left(\frac{5}{6}c-\frac{2}{7}c\right)$$

Combine \frac{5}{6}c and -\frac{2}{7}c to get \frac{23}{42}c.

$$\frac{14}{69}a^{2}b^{3}c\times \frac{23}{42}c$$

Multiply \frac{14}{69} and \frac{23}{42} to get \frac{1}{9}.

$$\frac{1}{9}a^{2}b^{3}cc$$

Multiply c and c to get c^{2}.

$$\frac{1}{9}a^{2}b^{3}c^{2}$$