Solve 9(3c-9/7c)(2/3c+11/4c)(c+1/6c)

$$9 ( 3 c - \frac { 9 } { 7 } c ) ( \frac { 2 } { 3 } c + \frac { 11 } { 4 } c ) ( c + \frac { 1 } { 6 } c )$$

Evaluate

$$\frac{123c^{3}}{2}$$

Solution Steps

Combine 3c and -\frac{9}{7}c to get \frac{12}{7}c.

$$9\times \frac{12}{7}c\left(\frac{2}{3}c+\frac{11}{4}c\right)\left(c+\frac{1}{6}c\right)$$

Express 9\times \frac{12}{7} as a single fraction.

$$\frac{9\times 12}{7}c\left(\frac{2}{3}c+\frac{11}{4}c\right)\left(c+\frac{1}{6}c\right)$$

Multiply 9 and 12 to get 108.

$$\frac{108}{7}c\left(\frac{2}{3}c+\frac{11}{4}c\right)\left(c+\frac{1}{6}c\right)$$

Combine \frac{2}{3}c and \frac{11}{4}c to get \frac{41}{12}c.

$$\frac{108}{7}c\times \frac{41}{12}c\left(c+\frac{1}{6}c\right)$$

Multiply \frac{108}{7} times \frac{41}{12} by multiplying numerator times numerator and denominator times denominator.

$$\frac{108\times 41}{7\times 12}cc\left(c+\frac{1}{6}c\right)$$

Do the multiplications in the fraction \frac{108\times 41}{7\times 12}.

$$\frac{4428}{84}cc\left(c+\frac{1}{6}c\right)$$

Reduce the fraction \frac{4428}{84} to lowest terms by extracting and canceling out 12.

$$\frac{369}{7}cc\left(c+\frac{1}{6}c\right)$$

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

$$\frac{369}{7}c^{2}\left(c+\frac{1}{6}c\right)$$

Combine c and \frac{1}{6}c to get \frac{7}{6}c.

$$\frac{369}{7}c^{2}\times \frac{7}{6}c$$

Multiply \frac{369}{7} times \frac{7}{6} by multiplying numerator times numerator and denominator times denominator.

$$\frac{369\times 7}{7\times 6}c^{2}c$$

Cancel out 7 in both numerator and denominator.

$$\frac{369}{6}c^{2}c$$

Reduce the fraction \frac{369}{6} to lowest terms by extracting and canceling out 3.

$$\frac{123}{2}c^{2}c$$

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

$$\frac{123}{2}c^{3}$$

Expand

$$\frac{123c^{3}}{2}$$

Solution Steps

Combine 3c and -\frac{9}{7}c to get \frac{12}{7}c.

$$9\times \frac{12}{7}c\left(\frac{2}{3}c+\frac{11}{4}c\right)\left(c+\frac{1}{6}c\right)$$

Express 9\times \frac{12}{7} as a single fraction.

$$\frac{9\times 12}{7}c\left(\frac{2}{3}c+\frac{11}{4}c\right)\left(c+\frac{1}{6}c\right)$$

Multiply 9 and 12 to get 108.

$$\frac{108}{7}c\left(\frac{2}{3}c+\frac{11}{4}c\right)\left(c+\frac{1}{6}c\right)$$

Combine \frac{2}{3}c and \frac{11}{4}c to get \frac{41}{12}c.

$$\frac{108}{7}c\times \frac{41}{12}c\left(c+\frac{1}{6}c\right)$$

Multiply \frac{108}{7} times \frac{41}{12} by multiplying numerator times numerator and denominator times denominator.

$$\frac{108\times 41}{7\times 12}cc\left(c+\frac{1}{6}c\right)$$

Do the multiplications in the fraction \frac{108\times 41}{7\times 12}.

$$\frac{4428}{84}cc\left(c+\frac{1}{6}c\right)$$

Reduce the fraction \frac{4428}{84} to lowest terms by extracting and canceling out 12.

$$\frac{369}{7}cc\left(c+\frac{1}{6}c\right)$$

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

$$\frac{369}{7}c^{2}\left(c+\frac{1}{6}c\right)$$

Combine c and \frac{1}{6}c to get \frac{7}{6}c.

$$\frac{369}{7}c^{2}\times \frac{7}{6}c$$

Multiply \frac{369}{7} times \frac{7}{6} by multiplying numerator times numerator and denominator times denominator.

$$\frac{369\times 7}{7\times 6}c^{2}c$$

Cancel out 7 in both numerator and denominator.

$$\frac{369}{6}c^{2}c$$

Reduce the fraction \frac{369}{6} to lowest terms by extracting and canceling out 3.

$$\frac{123}{2}c^{2}c$$

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

$$\frac{123}{2}c^{3}$$