Solve 1/2*(6-3/4t)*(8-t)

$$\frac { 1 } { 2 } \cdot ( 6 - \frac { 3 } { 4 } t ) \cdot ( 8 - t )$$

Evaluate

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

Solution Steps

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

$$\left(\frac{1}{2}\times 6+\frac{1}{2}\left(-\frac{3}{4}\right)t\right)\left(8-t\right)$$

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

$$\left(\frac{6}{2}+\frac{1}{2}\left(-\frac{3}{4}\right)t\right)\left(8-t\right)$$

Divide 6 by 2 to get 3.

$$\left(3+\frac{1}{2}\left(-\frac{3}{4}\right)t\right)\left(8-t\right)$$

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

$$\left(3+\frac{1\left(-3\right)}{2\times 4}t\right)\left(8-t\right)$$

Do the multiplications in the fraction \frac{1\left(-3\right)}{2\times 4}.

$$\left(3+\frac{-3}{8}t\right)\left(8-t\right)$$

Fraction \frac{-3}{8} can be rewritten as -\frac{3}{8} by extracting the negative sign.

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

Apply the distributive property by multiplying each term of 3-\frac{3}{8}t by each term of 8-t.

$$24-3t-\frac{3}{8}t\times 8-\frac{3}{8}t\left(-1\right)t$$

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

$$24-3t-\frac{3}{8}t\times 8-\frac{3}{8}t^{2}\left(-1\right)$$

Cancel out 8 and 8.

$$24-3t-3t-\frac{3}{8}t^{2}\left(-1\right)$$

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

$$24-6t-\frac{3}{8}t^{2}\left(-1\right)$$

Multiply -\frac{3}{8} and -1 to get \frac{3}{8}.

$$24-6t+\frac{3}{8}t^{2}$$

Expand

$$\frac{3t^{2}}{8}-6t+24$$

Solution Steps

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

$$\left(\frac{1}{2}\times 6+\frac{1}{2}\left(-\frac{3}{4}\right)t\right)\left(8-t\right)$$

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

$$\left(\frac{6}{2}+\frac{1}{2}\left(-\frac{3}{4}\right)t\right)\left(8-t\right)$$

Divide 6 by 2 to get 3.

$$\left(3+\frac{1}{2}\left(-\frac{3}{4}\right)t\right)\left(8-t\right)$$

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

$$\left(3+\frac{1\left(-3\right)}{2\times 4}t\right)\left(8-t\right)$$

Do the multiplications in the fraction \frac{1\left(-3\right)}{2\times 4}.

$$\left(3+\frac{-3}{8}t\right)\left(8-t\right)$$

Fraction \frac{-3}{8} can be rewritten as -\frac{3}{8} by extracting the negative sign.

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

Apply the distributive property by multiplying each term of 3-\frac{3}{8}t by each term of 8-t.

$$24-3t-\frac{3}{8}t\times 8-\frac{3}{8}t\left(-1\right)t$$

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

$$24-3t-\frac{3}{8}t\times 8-\frac{3}{8}t^{2}\left(-1\right)$$

Cancel out 8 and 8.

$$24-3t-3t-\frac{3}{8}t^{2}\left(-1\right)$$

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

$$24-6t-\frac{3}{8}t^{2}\left(-1\right)$$

Multiply -\frac{3}{8} and -1 to get \frac{3}{8}.

$$24-6t+\frac{3}{8}t^{2}$$