Solve 16-1/2left(8-tright)left(-5/4t+10right)

$$16- \frac{ 1 }{ 2 } \left( 8-t \right) \left( - \frac{ 5 }{ 4 } t+10 \right)$$

Evaluate

$$-\frac{5\left(8-t\right)^{2}}{8}+16$$

Solution Steps

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

$$16-\frac{1}{2}\left(8-t\right)\left(-\frac{5}{4}t+10\right)$$

Use the distributive property to multiply -\frac{1}{2} by 8-t.

$$16+\left(-\frac{1}{2}\times 8-\frac{1}{2}\left(-1\right)t\right)\left(-\frac{5}{4}t+10\right)$$

Express -\frac{1}{2}\times 8 as a single fraction.

$$16+\left(\frac{-8}{2}-\frac{1}{2}\left(-1\right)t\right)\left(-\frac{5}{4}t+10\right)$$

Divide -8 by 2 to get -4.

$$16+\left(-4-\frac{1}{2}\left(-1\right)t\right)\left(-\frac{5}{4}t+10\right)$$

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

$$16+\left(-4+\frac{1}{2}t\right)\left(-\frac{5}{4}t+10\right)$$

Apply the distributive property by multiplying each term of -4+\frac{1}{2}t by each term of -\frac{5}{4}t+10.

$$16-4\left(-\frac{5}{4}\right)t-40+\frac{1}{2}t\left(-\frac{5}{4}\right)t+\frac{1}{2}t\times 10$$

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

$$16-4\left(-\frac{5}{4}\right)t-40+\frac{1}{2}t^{2}\left(-\frac{5}{4}\right)+\frac{1}{2}t\times 10$$

Multiply -4 times -\frac{5}{4}.

$$16+5t-40+\frac{1}{2}t^{2}\left(-\frac{5}{4}\right)+\frac{1}{2}t\times 10$$

Multiply \frac{1}{2} times -\frac{5}{4} by multiplying numerator times numerator and denominator times denominator.

$$16+5t-40+\frac{1\left(-5\right)}{2\times 4}t^{2}+\frac{1}{2}t\times 10$$

Do the multiplications in the fraction \frac{1\left(-5\right)}{2\times 4}.

$$16+5t-40+\frac{-5}{8}t^{2}+\frac{1}{2}t\times 10$$

Fraction \frac{-5}{8} can be rewritten as -\frac{5}{8} by extracting the negative sign.

$$16+5t-40-\frac{5}{8}t^{2}+\frac{1}{2}t\times 10$$

Multiply \frac{1}{2} and 10 to get \frac{10}{2}.

$$16+5t-40-\frac{5}{8}t^{2}+\frac{10}{2}t$$

Divide 10 by 2 to get 5.

$$16+5t-40-\frac{5}{8}t^{2}+5t$$

Combine 5t and 5t to get 10t.

$$16+10t-40-\frac{5}{8}t^{2}$$

Subtract 40 from 16 to get -24.

$$-24+10t-\frac{5}{8}t^{2}$$

Expand

$$-\frac{5t^{2}}{8}+10t-24$$

Solution Steps

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

$$16-\frac{1}{2}\left(8-t\right)\left(-\frac{5}{4}t+10\right)$$

Use the distributive property to multiply -\frac{1}{2} by 8-t.

$$16+\left(-\frac{1}{2}\times 8-\frac{1}{2}\left(-1\right)t\right)\left(-\frac{5}{4}t+10\right)$$

Express -\frac{1}{2}\times 8 as a single fraction.

$$16+\left(\frac{-8}{2}-\frac{1}{2}\left(-1\right)t\right)\left(-\frac{5}{4}t+10\right)$$

Divide -8 by 2 to get -4.

$$16+\left(-4-\frac{1}{2}\left(-1\right)t\right)\left(-\frac{5}{4}t+10\right)$$

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

$$16+\left(-4+\frac{1}{2}t\right)\left(-\frac{5}{4}t+10\right)$$

Apply the distributive property by multiplying each term of -4+\frac{1}{2}t by each term of -\frac{5}{4}t+10.

$$16-4\left(-\frac{5}{4}\right)t-40+\frac{1}{2}t\left(-\frac{5}{4}\right)t+\frac{1}{2}t\times 10$$

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

$$16-4\left(-\frac{5}{4}\right)t-40+\frac{1}{2}t^{2}\left(-\frac{5}{4}\right)+\frac{1}{2}t\times 10$$

Multiply -4 times -\frac{5}{4}.

$$16+5t-40+\frac{1}{2}t^{2}\left(-\frac{5}{4}\right)+\frac{1}{2}t\times 10$$

Multiply \frac{1}{2} times -\frac{5}{4} by multiplying numerator times numerator and denominator times denominator.

$$16+5t-40+\frac{1\left(-5\right)}{2\times 4}t^{2}+\frac{1}{2}t\times 10$$

Do the multiplications in the fraction \frac{1\left(-5\right)}{2\times 4}.

$$16+5t-40+\frac{-5}{8}t^{2}+\frac{1}{2}t\times 10$$

Fraction \frac{-5}{8} can be rewritten as -\frac{5}{8} by extracting the negative sign.

$$16+5t-40-\frac{5}{8}t^{2}+\frac{1}{2}t\times 10$$

Multiply \frac{1}{2} and 10 to get \frac{10}{2}.

$$16+5t-40-\frac{5}{8}t^{2}+\frac{10}{2}t$$

Divide 10 by 2 to get 5.

$$16+5t-40-\frac{5}{8}t^{2}+5t$$

Combine 5t and 5t to get 10t.

$$16+10t-40-\frac{5}{8}t^{2}$$

Subtract 40 from 16 to get -24.

$$-24+10t-\frac{5}{8}t^{2}$$