Solve 6-3t/50(8-4/5t)(10-t)

$$6 - \frac { 3 t } { 50 } ( 8 - \frac { 4 } { 5 } t ) ( 10 - t )$$

Evaluate

$$-\frac{6t\left(10-t\right)^{2}}{125}+6$$

Short Solution Steps

Express \frac{3t}{50}\left(10-t\right) as a single fraction.

$$6-\frac{3t\left(10-t\right)}{50}\left(8-\frac{4}{5}t\right)$$

Use the distributive property to multiply \frac{3t\left(10-t\right)}{50} by 8-\frac{4}{5}t.

$$6-\left(8\times \frac{3t\left(10-t\right)}{50}+\frac{3t\left(10-t\right)}{50}\left(-\frac{4}{5}\right)t\right)$$

Use the distributive property to multiply 3t by 10-t.

$$6-\left(8\times \frac{30t-3t^{2}}{50}+\frac{3t\left(10-t\right)}{50}\left(-\frac{4}{5}\right)t\right)$$

Express 8\times \frac{30t-3t^{2}}{50} as a single fraction.

$$6-\left(\frac{8\left(30t-3t^{2}\right)}{50}+\frac{3t\left(10-t\right)}{50}\left(-\frac{4}{5}\right)t\right)$$

Use the distributive property to multiply 3t by 10-t.

$$6-\left(\frac{8\left(30t-3t^{2}\right)}{50}+\frac{30t-3t^{2}}{50}\left(-\frac{4}{5}\right)t\right)$$

Multiply \frac{30t-3t^{2}}{50} times -\frac{4}{5} by multiplying numerator times numerator and denominator times denominator.

$$6-\left(\frac{8\left(30t-3t^{2}\right)}{50}+\frac{-\left(30t-3t^{2}\right)\times 4}{50\times 5}t\right)$$

Cancel out 2 in both numerator and denominator.

$$6-\left(\frac{8\left(30t-3t^{2}\right)}{50}+\frac{-2\left(-3t^{2}+30t\right)}{5\times 25}t\right)$$

Express \frac{-2\left(-3t^{2}+30t\right)}{5\times 25}t as a single fraction.

$$6-\left(\frac{8\left(30t-3t^{2}\right)}{50}+\frac{-2\left(-3t^{2}+30t\right)t}{5\times 25}\right)$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 50 and 5\times 25 is 250. Multiply \frac{8\left(30t-3t^{2}\right)}{50} times \frac{5}{5}. Multiply \frac{-2\left(-3t^{2}+30t\right)t}{5\times 25} times \frac{2}{2}.

$$6-\left(\frac{5\times 8\left(30t-3t^{2}\right)}{250}+\frac{2\left(-1\right)\times 2\left(-3t^{2}+30t\right)t}{250}\right)$$

Since \frac{5\times 8\left(30t-3t^{2}\right)}{250} and \frac{2\left(-1\right)\times 2\left(-3t^{2}+30t\right)t}{250} have the same denominator, add them by adding their numerators.

$$6-\frac{5\times 8\left(30t-3t^{2}\right)+2\left(-1\right)\times 2\left(-3t^{2}+30t\right)t}{250}$$

Do the multiplications in 5\times 8\left(30t-3t^{2}\right)+2\left(-1\right)\times 2\left(-3t^{2}+30t\right)t.

$$6-\frac{1200t-120t^{2}+12t^{3}-120t^{2}}{250}$$

Combine like terms in 1200t-120t^{2}+12t^{3}-120t^{2}.

$$6-\frac{1200t-240t^{2}+12t^{3}}{250}$$

To add or subtract expressions, expand them to make their denominators the same. Multiply 6 times \frac{250}{250}.

$$\frac{6\times 250}{250}-\frac{1200t-240t^{2}+12t^{3}}{250}$$

Since \frac{6\times 250}{250} and \frac{1200t-240t^{2}+12t^{3}}{250} have the same denominator, subtract them by subtracting their numerators.

$$\frac{6\times 250-\left(1200t-240t^{2}+12t^{3}\right)}{250}$$

Do the multiplications in 6\times 250-\left(1200t-240t^{2}+12t^{3}\right).

$$\frac{1500-1200t+240t^{2}-12t^{3}}{250}$$

Expand

$$-\frac{6t^{3}}{125}+\frac{24t^{2}}{25}-\frac{24t}{5}+6$$

Short Solution Steps

Express \frac{3t}{50}\left(10-t\right) as a single fraction.

$$6-\frac{3t\left(10-t\right)}{50}\left(8-\frac{4}{5}t\right)$$

Use the distributive property to multiply \frac{3t\left(10-t\right)}{50} by 8-\frac{4}{5}t.

$$6-\left(8\times \frac{3t\left(10-t\right)}{50}+\frac{3t\left(10-t\right)}{50}\left(-\frac{4}{5}\right)t\right)$$

Use the distributive property to multiply 3t by 10-t.

$$6-\left(8\times \frac{30t-3t^{2}}{50}+\frac{3t\left(10-t\right)}{50}\left(-\frac{4}{5}\right)t\right)$$

Express 8\times \frac{30t-3t^{2}}{50} as a single fraction.

$$6-\left(\frac{8\left(30t-3t^{2}\right)}{50}+\frac{3t\left(10-t\right)}{50}\left(-\frac{4}{5}\right)t\right)$$

Use the distributive property to multiply 3t by 10-t.

$$6-\left(\frac{8\left(30t-3t^{2}\right)}{50}+\frac{30t-3t^{2}}{50}\left(-\frac{4}{5}\right)t\right)$$

Multiply \frac{30t-3t^{2}}{50} times -\frac{4}{5} by multiplying numerator times numerator and denominator times denominator.

$$6-\left(\frac{8\left(30t-3t^{2}\right)}{50}+\frac{-\left(30t-3t^{2}\right)\times 4}{50\times 5}t\right)$$

Cancel out 2 in both numerator and denominator.

$$6-\left(\frac{8\left(30t-3t^{2}\right)}{50}+\frac{-2\left(-3t^{2}+30t\right)}{5\times 25}t\right)$$

Express \frac{-2\left(-3t^{2}+30t\right)}{5\times 25}t as a single fraction.

$$6-\left(\frac{8\left(30t-3t^{2}\right)}{50}+\frac{-2\left(-3t^{2}+30t\right)t}{5\times 25}\right)$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 50 and 5\times 25 is 250. Multiply \frac{8\left(30t-3t^{2}\right)}{50} times \frac{5}{5}. Multiply \frac{-2\left(-3t^{2}+30t\right)t}{5\times 25} times \frac{2}{2}.

$$6-\left(\frac{5\times 8\left(30t-3t^{2}\right)}{250}+\frac{2\left(-1\right)\times 2\left(-3t^{2}+30t\right)t}{250}\right)$$

Since \frac{5\times 8\left(30t-3t^{2}\right)}{250} and \frac{2\left(-1\right)\times 2\left(-3t^{2}+30t\right)t}{250} have the same denominator, add them by adding their numerators.

$$6-\frac{5\times 8\left(30t-3t^{2}\right)+2\left(-1\right)\times 2\left(-3t^{2}+30t\right)t}{250}$$

Do the multiplications in 5\times 8\left(30t-3t^{2}\right)+2\left(-1\right)\times 2\left(-3t^{2}+30t\right)t.

$$6-\frac{1200t-120t^{2}+12t^{3}-120t^{2}}{250}$$

Combine like terms in 1200t-120t^{2}+12t^{3}-120t^{2}.

$$6-\frac{1200t-240t^{2}+12t^{3}}{250}$$

To add or subtract expressions, expand them to make their denominators the same. Multiply 6 times \frac{250}{250}.

$$\frac{6\times 250}{250}-\frac{1200t-240t^{2}+12t^{3}}{250}$$

Since \frac{6\times 250}{250} and \frac{1200t-240t^{2}+12t^{3}}{250} have the same denominator, subtract them by subtracting their numerators.

$$\frac{6\times 250-\left(1200t-240t^{2}+12t^{3}\right)}{250}$$

Do the multiplications in 6\times 250-\left(1200t-240t^{2}+12t^{3}\right).

$$\frac{1500-1200t+240t^{2}-12t^{3}}{250}$$