Solve left(36-1/4tright)left(-1/2t+52right)=

$$\left( 36- \frac{ 1 }{ 4 } t \right) \left( - \frac{ 1 }{ 2 } t+52 \right) =$$

Evaluate

$$\frac{\left(t-144\right)\left(t-104\right)}{8}$$

Solution Steps

Apply the distributive property by multiplying each term of 36-\frac{1}{4}t by each term of -\frac{1}{2}t+52.

$$36\left(-\frac{1}{2}\right)t+1872-\frac{1}{4}t\left(-\frac{1}{2}\right)t-\frac{1}{4}t\times 52$$

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

$$36\left(-\frac{1}{2}\right)t+1872-\frac{1}{4}t^{2}\left(-\frac{1}{2}\right)-\frac{1}{4}t\times 52$$

Express 36\left(-\frac{1}{2}\right) as a single fraction.

$$\frac{36\left(-1\right)}{2}t+1872-\frac{1}{4}t^{2}\left(-\frac{1}{2}\right)-\frac{1}{4}t\times 52$$

Multiply 36 and -1 to get -36.

$$\frac{-36}{2}t+1872-\frac{1}{4}t^{2}\left(-\frac{1}{2}\right)-\frac{1}{4}t\times 52$$

Divide -36 by 2 to get -18.

$$-18t+1872-\frac{1}{4}t^{2}\left(-\frac{1}{2}\right)-\frac{1}{4}t\times 52$$

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

$$-18t+1872+\frac{-\left(-1\right)}{4\times 2}t^{2}-\frac{1}{4}t\times 52$$

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

$$-18t+1872+\frac{1}{8}t^{2}-\frac{1}{4}t\times 52$$

Express -\frac{1}{4}\times 52 as a single fraction.

$$-18t+1872+\frac{1}{8}t^{2}+\frac{-52}{4}t$$

Divide -52 by 4 to get -13.

$$-18t+1872+\frac{1}{8}t^{2}-13t$$

Combine -18t and -13t to get -31t.

$$-31t+1872+\frac{1}{8}t^{2}$$

Expand

$$\frac{t^{2}}{8}-31t+1872$$

Solution Steps

Apply the distributive property by multiplying each term of 36-\frac{1}{4}t by each term of -\frac{1}{2}t+52.

$$36\left(-\frac{1}{2}\right)t+1872-\frac{1}{4}t\left(-\frac{1}{2}\right)t-\frac{1}{4}t\times 52$$

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

$$36\left(-\frac{1}{2}\right)t+1872-\frac{1}{4}t^{2}\left(-\frac{1}{2}\right)-\frac{1}{4}t\times 52$$

Express 36\left(-\frac{1}{2}\right) as a single fraction.

$$\frac{36\left(-1\right)}{2}t+1872-\frac{1}{4}t^{2}\left(-\frac{1}{2}\right)-\frac{1}{4}t\times 52$$

Multiply 36 and -1 to get -36.

$$\frac{-36}{2}t+1872-\frac{1}{4}t^{2}\left(-\frac{1}{2}\right)-\frac{1}{4}t\times 52$$

Divide -36 by 2 to get -18.

$$-18t+1872-\frac{1}{4}t^{2}\left(-\frac{1}{2}\right)-\frac{1}{4}t\times 52$$

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

$$-18t+1872+\frac{-\left(-1\right)}{4\times 2}t^{2}-\frac{1}{4}t\times 52$$

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

$$-18t+1872+\frac{1}{8}t^{2}-\frac{1}{4}t\times 52$$

Express -\frac{1}{4}\times 52 as a single fraction.

$$-18t+1872+\frac{1}{8}t^{2}+\frac{-52}{4}t$$

Divide -52 by 4 to get -13.

$$-18t+1872+\frac{1}{8}t^{2}-13t$$

Combine -18t and -13t to get -31t.

$$-31t+1872+\frac{1}{8}t^{2}$$