Solve 20left(t^3/360-t^2/7+2t+2right)

$$20 \left( \frac{ { t }^{ 3 } }{ 360 } - \frac{ { t }^{ 2 } }{ 7 } +2t+2 \right)$$

Evaluate

$$\frac{t^{3}}{18}-\frac{20t^{2}}{7}+40t+40$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 360 and 7 is 2520. Multiply \frac{t^{3}}{360} times \frac{7}{7}. Multiply \frac{t^{2}}{7} times \frac{360}{360}.

$$20\left(\frac{7t^{3}}{2520}-\frac{360t^{2}}{2520}+2t+2\right)$$

Since \frac{7t^{3}}{2520} and \frac{360t^{2}}{2520} have the same denominator, subtract them by subtracting their numerators.

$$20\left(\frac{7t^{3}-360t^{2}}{2520}+2t+2\right)$$

To add or subtract expressions, expand them to make their denominators the same. Multiply 2t+2 times \frac{2520}{2520}.

$$20\left(\frac{7t^{3}-360t^{2}}{2520}+\frac{2520\left(2t+2\right)}{2520}\right)$$

Since \frac{7t^{3}-360t^{2}}{2520} and \frac{2520\left(2t+2\right)}{2520} have the same denominator, add them by adding their numerators.

$$20\times \frac{7t^{3}-360t^{2}+2520\left(2t+2\right)}{2520}$$

Do the multiplications in 7t^{3}-360t^{2}+2520\left(2t+2\right).

$$20\times \frac{7t^{3}-360t^{2}+5040t+5040}{2520}$$

Cancel out 2520, the greatest common factor in 20 and 2520.

$$\frac{7t^{3}-360t^{2}+5040t+5040}{126}$$

Expand

$$\frac{t^{3}}{18}-\frac{20t^{2}}{7}+40t+40$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 360 and 7 is 2520. Multiply \frac{t^{3}}{360} times \frac{7}{7}. Multiply \frac{t^{2}}{7} times \frac{360}{360}.

$$20\left(\frac{7t^{3}}{2520}-\frac{360t^{2}}{2520}+2t+2\right)$$

Since \frac{7t^{3}}{2520} and \frac{360t^{2}}{2520} have the same denominator, subtract them by subtracting their numerators.

$$20\left(\frac{7t^{3}-360t^{2}}{2520}+2t+2\right)$$

To add or subtract expressions, expand them to make their denominators the same. Multiply 2t+2 times \frac{2520}{2520}.

$$20\left(\frac{7t^{3}-360t^{2}}{2520}+\frac{2520\left(2t+2\right)}{2520}\right)$$

Since \frac{7t^{3}-360t^{2}}{2520} and \frac{2520\left(2t+2\right)}{2520} have the same denominator, add them by adding their numerators.

$$20\times \frac{7t^{3}-360t^{2}+2520\left(2t+2\right)}{2520}$$

Do the multiplications in 7t^{3}-360t^{2}+2520\left(2t+2\right).

$$20\times \frac{7t^{3}-360t^{2}+5040t+5040}{2520}$$

Cancel out 2520, the greatest common factor in 20 and 2520.

$$\frac{7t^{3}-360t^{2}+5040t+5040}{126}$$