Solve (2a^2/9-1/7)(3a/5-2/5)

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

Evaluate

$$\frac{\left(3a-2\right)\left(14a^{2}-9\right)}{315}$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 9 and 7 is 63. Multiply \frac{2a^{2}}{9} times \frac{7}{7}. Multiply \frac{1}{7} times \frac{9}{9}.

$$\left(\frac{7\times 2a^{2}}{63}-\frac{9}{63}\right)\left(\frac{3a}{5}-\frac{2}{5}\right)$$

Since \frac{7\times 2a^{2}}{63} and \frac{9}{63} have the same denominator, subtract them by subtracting their numerators.

$$\frac{7\times 2a^{2}-9}{63}\left(\frac{3a}{5}-\frac{2}{5}\right)$$

Do the multiplications in 7\times 2a^{2}-9.

$$\frac{14a^{2}-9}{63}\left(\frac{3a}{5}-\frac{2}{5}\right)$$

Since \frac{3a}{5} and \frac{2}{5} have the same denominator, subtract them by subtracting their numerators.

$$\frac{14a^{2}-9}{63}\times \frac{3a-2}{5}$$

Multiply \frac{14a^{2}-9}{63} times \frac{3a-2}{5} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\left(14a^{2}-9\right)\left(3a-2\right)}{63\times 5}$$

Multiply 63 and 5 to get 315.

$$\frac{\left(14a^{2}-9\right)\left(3a-2\right)}{315}$$

Use the distributive property to multiply 14a^{2}-9 by 3a-2.

$$\frac{42a^{3}-28a^{2}-27a+18}{315}$$

Expand

$$\frac{2a^{3}}{15}-\frac{4a^{2}}{45}-\frac{3a}{35}+\frac{2}{35}$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 9 and 7 is 63. Multiply \frac{2a^{2}}{9} times \frac{7}{7}. Multiply \frac{1}{7} times \frac{9}{9}.

$$\left(\frac{7\times 2a^{2}}{63}-\frac{9}{63}\right)\left(\frac{3a}{5}-\frac{2}{5}\right)$$

Since \frac{7\times 2a^{2}}{63} and \frac{9}{63} have the same denominator, subtract them by subtracting their numerators.

$$\frac{7\times 2a^{2}-9}{63}\left(\frac{3a}{5}-\frac{2}{5}\right)$$

Do the multiplications in 7\times 2a^{2}-9.

$$\frac{14a^{2}-9}{63}\left(\frac{3a}{5}-\frac{2}{5}\right)$$

Since \frac{3a}{5} and \frac{2}{5} have the same denominator, subtract them by subtracting their numerators.

$$\frac{14a^{2}-9}{63}\times \frac{3a-2}{5}$$

Multiply \frac{14a^{2}-9}{63} times \frac{3a-2}{5} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\left(14a^{2}-9\right)\left(3a-2\right)}{63\times 5}$$

Multiply 63 and 5 to get 315.

$$\frac{\left(14a^{2}-9\right)\left(3a-2\right)}{315}$$

Use the distributive property to multiply 14a^{2}-9 by 3a-2.

$$\frac{42a^{3}-28a^{2}-27a+18}{315}$$