Solve (3-3/4t)(4-t)1/2

$$( 3 - \frac { 3 } { 4 } t ) ( 4 - t ) \frac { 1 } { 2 }$$

Evaluate

$$\frac{3\left(4-t\right)^{2}}{8}$$

Solution Steps

Apply the distributive property by multiplying each term of 3-\frac{3}{4}t by each term of 4-t.

$$\left(12-3t-\frac{3}{4}t\times 4-\frac{3}{4}t\left(-1\right)t\right)\times \frac{1}{2}$$

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

$$\left(12-3t-\frac{3}{4}t\times 4-\frac{3}{4}t^{2}\left(-1\right)\right)\times \frac{1}{2}$$

Cancel out 4 and 4.

$$\left(12-3t-3t-\frac{3}{4}t^{2}\left(-1\right)\right)\times \frac{1}{2}$$

Combine -3t and -3t to get -6t.

$$\left(12-6t-\frac{3}{4}t^{2}\left(-1\right)\right)\times \frac{1}{2}$$

Multiply -\frac{3}{4} and -1 to get \frac{3}{4}.

$$\left(12-6t+\frac{3}{4}t^{2}\right)\times \frac{1}{2}$$

Use the distributive property to multiply 12-6t+\frac{3}{4}t^{2} by \frac{1}{2}.

$$12\times \frac{1}{2}-6t\times \frac{1}{2}+\frac{3}{4}t^{2}\times \frac{1}{2}$$

Multiply 12 and \frac{1}{2} to get \frac{12}{2}.

$$\frac{12}{2}-6t\times \frac{1}{2}+\frac{3}{4}t^{2}\times \frac{1}{2}$$

Divide 12 by 2 to get 6.

$$6-6t\times \frac{1}{2}+\frac{3}{4}t^{2}\times \frac{1}{2}$$

Multiply -6 and \frac{1}{2} to get \frac{-6}{2}.

$$6+\frac{-6}{2}t+\frac{3}{4}t^{2}\times \frac{1}{2}$$

Divide -6 by 2 to get -3.

$$6-3t+\frac{3}{4}t^{2}\times \frac{1}{2}$$

Multiply \frac{3}{4} times \frac{1}{2} by multiplying numerator times numerator and denominator times denominator.

$$6-3t+\frac{3\times 1}{4\times 2}t^{2}$$

Do the multiplications in the fraction \frac{3\times 1}{4\times 2}.

$$6-3t+\frac{3}{8}t^{2}$$

Expand

$$\frac{3t^{2}}{8}-3t+6$$

Solution Steps

Apply the distributive property by multiplying each term of 3-\frac{3}{4}t by each term of 4-t.

$$\left(12-3t-\frac{3}{4}t\times 4-\frac{3}{4}t\left(-1\right)t\right)\times \frac{1}{2}$$

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

$$\left(12-3t-\frac{3}{4}t\times 4-\frac{3}{4}t^{2}\left(-1\right)\right)\times \frac{1}{2}$$

Cancel out 4 and 4.

$$\left(12-3t-3t-\frac{3}{4}t^{2}\left(-1\right)\right)\times \frac{1}{2}$$

Combine -3t and -3t to get -6t.

$$\left(12-6t-\frac{3}{4}t^{2}\left(-1\right)\right)\times \frac{1}{2}$$

Multiply -\frac{3}{4} and -1 to get \frac{3}{4}.

$$\left(12-6t+\frac{3}{4}t^{2}\right)\times \frac{1}{2}$$

Use the distributive property to multiply 12-6t+\frac{3}{4}t^{2} by \frac{1}{2}.

$$12\times \frac{1}{2}-6t\times \frac{1}{2}+\frac{3}{4}t^{2}\times \frac{1}{2}$$

Multiply 12 and \frac{1}{2} to get \frac{12}{2}.

$$\frac{12}{2}-6t\times \frac{1}{2}+\frac{3}{4}t^{2}\times \frac{1}{2}$$

Divide 12 by 2 to get 6.

$$6-6t\times \frac{1}{2}+\frac{3}{4}t^{2}\times \frac{1}{2}$$

Multiply -6 and \frac{1}{2} to get \frac{-6}{2}.

$$6+\frac{-6}{2}t+\frac{3}{4}t^{2}\times \frac{1}{2}$$

Divide -6 by 2 to get -3.

$$6-3t+\frac{3}{4}t^{2}\times \frac{1}{2}$$

Multiply \frac{3}{4} times \frac{1}{2} by multiplying numerator times numerator and denominator times denominator.

$$6-3t+\frac{3\times 1}{4\times 2}t^{2}$$

Do the multiplications in the fraction \frac{3\times 1}{4\times 2}.

$$6-3t+\frac{3}{8}t^{2}$$