Solve (1-0)(t-3)(t-5)(t-8)/(13-0)(13-3)(13-8)(13-5)=

$$\frac { ( 1 - 0 ) ( t - 3 ) ( t - 5 ) ( t - 8 ) } { ( 13 - 0 ) ( 13 - 3 ) ( 13 - 8 ) ( 13 - 5 ) } =$$

Evaluate

$$\frac{\left(t-8\right)\left(t-5\right)\left(t-3\right)}{5200}$$

Solution Steps

Subtract 0 from 1 to get 1.

$$\frac{1\left(t-3\right)\left(t-5\right)\left(t-8\right)}{\left(13-0\right)\left(13-3\right)\left(13-8\right)\left(13-5\right)}$$

Subtract 0 from 13 to get 13.

$$\frac{1\left(t-3\right)\left(t-5\right)\left(t-8\right)}{13\left(13-3\right)\left(13-8\right)\left(13-5\right)}$$

Subtract 3 from 13 to get 10.

$$\frac{1\left(t-3\right)\left(t-5\right)\left(t-8\right)}{13\times 10\left(13-8\right)\left(13-5\right)}$$

Multiply 13 and 10 to get 130.

$$\frac{1\left(t-3\right)\left(t-5\right)\left(t-8\right)}{130\left(13-8\right)\left(13-5\right)}$$

Subtract 8 from 13 to get 5.

$$\frac{1\left(t-3\right)\left(t-5\right)\left(t-8\right)}{130\times 5\left(13-5\right)}$$

Multiply 130 and 5 to get 650.

$$\frac{1\left(t-3\right)\left(t-5\right)\left(t-8\right)}{650\left(13-5\right)}$$

Subtract 5 from 13 to get 8.

$$\frac{1\left(t-3\right)\left(t-5\right)\left(t-8\right)}{650\times 8}$$

Multiply 650 and 8 to get 5200.

$$\frac{1\left(t-3\right)\left(t-5\right)\left(t-8\right)}{5200}$$

Use the distributive property to multiply 1 by t-3.

$$\frac{\left(t-3\right)\left(t-5\right)\left(t-8\right)}{5200}$$

Apply the distributive property by multiplying each term of t-3 by each term of t-5.

$$\frac{\left(t^{2}-5t-3t+15\right)\left(t-8\right)}{5200}$$

Combine -5t and -3t to get -8t.

$$\frac{\left(t^{2}-8t+15\right)\left(t-8\right)}{5200}$$

Apply the distributive property by multiplying each term of t^{2}-8t+15 by each term of t-8.

$$\frac{t^{3}-8t^{2}-8t^{2}+64t+15t-120}{5200}$$

Combine -8t^{2} and -8t^{2} to get -16t^{2}.

$$\frac{t^{3}-16t^{2}+64t+15t-120}{5200}$$

Combine 64t and 15t to get 79t.

$$\frac{t^{3}-16t^{2}+79t-120}{5200}$$

Expand

$$\frac{t^{3}}{5200}-\frac{t^{2}}{325}+\frac{79t}{5200}-\frac{3}{130}$$

Solution Steps

Subtract 0 from 1 to get 1.

$$\frac{1\left(t-3\right)\left(t-5\right)\left(t-8\right)}{\left(13-0\right)\left(13-3\right)\left(13-8\right)\left(13-5\right)}$$

Subtract 0 from 13 to get 13.

$$\frac{1\left(t-3\right)\left(t-5\right)\left(t-8\right)}{13\left(13-3\right)\left(13-8\right)\left(13-5\right)}$$

Subtract 3 from 13 to get 10.

$$\frac{1\left(t-3\right)\left(t-5\right)\left(t-8\right)}{13\times 10\left(13-8\right)\left(13-5\right)}$$

Multiply 13 and 10 to get 130.

$$\frac{1\left(t-3\right)\left(t-5\right)\left(t-8\right)}{130\left(13-8\right)\left(13-5\right)}$$

Subtract 8 from 13 to get 5.

$$\frac{1\left(t-3\right)\left(t-5\right)\left(t-8\right)}{130\times 5\left(13-5\right)}$$

Multiply 130 and 5 to get 650.

$$\frac{1\left(t-3\right)\left(t-5\right)\left(t-8\right)}{650\left(13-5\right)}$$

Subtract 5 from 13 to get 8.

$$\frac{1\left(t-3\right)\left(t-5\right)\left(t-8\right)}{650\times 8}$$

Multiply 650 and 8 to get 5200.

$$\frac{1\left(t-3\right)\left(t-5\right)\left(t-8\right)}{5200}$$

Use the distributive property to multiply 1 by t-3.

$$\frac{\left(t-3\right)\left(t-5\right)\left(t-8\right)}{5200}$$

Apply the distributive property by multiplying each term of t-3 by each term of t-5.

$$\frac{\left(t^{2}-5t-3t+15\right)\left(t-8\right)}{5200}$$

Combine -5t and -3t to get -8t.

$$\frac{\left(t^{2}-8t+15\right)\left(t-8\right)}{5200}$$

Apply the distributive property by multiplying each term of t^{2}-8t+15 by each term of t-8.

$$\frac{t^{3}-8t^{2}-8t^{2}+64t+15t-120}{5200}$$

Combine -8t^{2} and -8t^{2} to get -16t^{2}.

$$\frac{t^{3}-16t^{2}+64t+15t-120}{5200}$$

Combine 64t and 15t to get 79t.

$$\frac{t^{3}-16t^{2}+79t-120}{5200}$$