Solve (10/3-3m^4/2)(3m^2/2+10/3)

$$( \frac { 10 } { 3 } - \frac { 3 m ^ { 4 } } { 2 } ) ( \frac { 3 m ^ { 2 } } { 2 } + \frac { 10 } { 3 } )$$

Evaluate

$$\frac{\left(9m^{2}+20\right)\left(20-9m^{4}\right)}{36}$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 3 and 2 is 6. Multiply \frac{10}{3} times \frac{2}{2}. Multiply \frac{3m^{4}}{2} times \frac{3}{3}.

$$\left(\frac{10\times 2}{6}-\frac{3\times 3m^{4}}{6}\right)\left(\frac{3m^{2}}{2}+\frac{10}{3}\right)$$

Since \frac{10\times 2}{6} and \frac{3\times 3m^{4}}{6} have the same denominator, subtract them by subtracting their numerators.

$$\frac{10\times 2-3\times 3m^{4}}{6}\left(\frac{3m^{2}}{2}+\frac{10}{3}\right)$$

Do the multiplications in 10\times 2-3\times 3m^{4}.

$$\frac{20-9m^{4}}{6}\left(\frac{3m^{2}}{2}+\frac{10}{3}\right)$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 2 and 3 is 6. Multiply \frac{3m^{2}}{2} times \frac{3}{3}. Multiply \frac{10}{3} times \frac{2}{2}.

$$\frac{20-9m^{4}}{6}\left(\frac{3\times 3m^{2}}{6}+\frac{10\times 2}{6}\right)$$

Since \frac{3\times 3m^{2}}{6} and \frac{10\times 2}{6} have the same denominator, add them by adding their numerators.

$$\frac{20-9m^{4}}{6}\times \frac{3\times 3m^{2}+10\times 2}{6}$$

Do the multiplications in 3\times 3m^{2}+10\times 2.

$$\frac{20-9m^{4}}{6}\times \frac{9m^{2}+20}{6}$$

Multiply \frac{20-9m^{4}}{6} times \frac{9m^{2}+20}{6} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\left(20-9m^{4}\right)\left(9m^{2}+20\right)}{6\times 6}$$

Multiply 6 and 6 to get 36.

$$\frac{\left(20-9m^{4}\right)\left(9m^{2}+20\right)}{36}$$

Use the distributive property to multiply 20-9m^{4} by 9m^{2}+20.

$$\frac{180m^{2}+400-81m^{6}-180m^{4}}{36}$$

Expand

$$-\frac{9m^{6}}{4}-5m^{4}+5m^{2}+\frac{100}{9}$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 3 and 2 is 6. Multiply \frac{10}{3} times \frac{2}{2}. Multiply \frac{3m^{4}}{2} times \frac{3}{3}.

$$\left(\frac{10\times 2}{6}-\frac{3\times 3m^{4}}{6}\right)\left(\frac{3m^{2}}{2}+\frac{10}{3}\right)$$

Since \frac{10\times 2}{6} and \frac{3\times 3m^{4}}{6} have the same denominator, subtract them by subtracting their numerators.

$$\frac{10\times 2-3\times 3m^{4}}{6}\left(\frac{3m^{2}}{2}+\frac{10}{3}\right)$$

Do the multiplications in 10\times 2-3\times 3m^{4}.

$$\frac{20-9m^{4}}{6}\left(\frac{3m^{2}}{2}+\frac{10}{3}\right)$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 2 and 3 is 6. Multiply \frac{3m^{2}}{2} times \frac{3}{3}. Multiply \frac{10}{3} times \frac{2}{2}.

$$\frac{20-9m^{4}}{6}\left(\frac{3\times 3m^{2}}{6}+\frac{10\times 2}{6}\right)$$

Since \frac{3\times 3m^{2}}{6} and \frac{10\times 2}{6} have the same denominator, add them by adding their numerators.

$$\frac{20-9m^{4}}{6}\times \frac{3\times 3m^{2}+10\times 2}{6}$$

Do the multiplications in 3\times 3m^{2}+10\times 2.

$$\frac{20-9m^{4}}{6}\times \frac{9m^{2}+20}{6}$$

Multiply \frac{20-9m^{4}}{6} times \frac{9m^{2}+20}{6} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\left(20-9m^{4}\right)\left(9m^{2}+20\right)}{6\times 6}$$

Multiply 6 and 6 to get 36.

$$\frac{\left(20-9m^{4}\right)\left(9m^{2}+20\right)}{36}$$

Use the distributive property to multiply 20-9m^{4} by 9m^{2}+20.

$$\frac{180m^{2}+400-81m^{6}-180m^{4}}{36}$$