Solve (x-4)*(x^2/4+x+4)+3*(x^2-x-1)*(x-2)+1

$$( x - 4 ) \cdot ( \frac { x ^ { 2 } } { 4 } + x + 4 ) + 3 \cdot ( x ^ { 2 } - x - 1 ) \cdot ( x - 2 ) + 1$$

Evaluate

$$\frac{13x^{3}}{4}-9x^{2}+3x-9$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Multiply x+4 times \frac{4}{4}.

$$\left(x-4\right)\left(\frac{x^{2}}{4}+\frac{4\left(x+4\right)}{4}\right)+3\left(x^{2}-x-1\right)\left(x-2\right)+1$$

Since \frac{x^{2}}{4} and \frac{4\left(x+4\right)}{4} have the same denominator, add them by adding their numerators.

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

Do the multiplications in x^{2}+4\left(x+4\right).

$$\left(x-4\right)\times \frac{x^{2}+4x+16}{4}+3\left(x^{2}-x-1\right)\left(x-2\right)+1$$

Express \left(x-4\right)\times \frac{x^{2}+4x+16}{4} as a single fraction.

$$\frac{\left(x-4\right)\left(x^{2}+4x+16\right)}{4}+3\left(x^{2}-x-1\right)\left(x-2\right)+1$$

Use the distributive property to multiply x-4 by x^{2}+4x+16 and combine like terms.

$$\frac{x^{3}-64}{4}+3\left(x^{2}-x-1\right)\left(x-2\right)+1$$

Use the distributive property to multiply 3 by x^{2}-x-1.

$$\frac{x^{3}-64}{4}+\left(3x^{2}-3x-3\right)\left(x-2\right)+1$$

Use the distributive property to multiply 3x^{2}-3x-3 by x-2 and combine like terms.

$$\frac{x^{3}-64}{4}+3x^{3}-9x^{2}+3x+6+1$$

Add 6 and 1 to get 7.

$$\frac{x^{3}-64}{4}+3x^{3}-9x^{2}+3x+7$$

To add or subtract expressions, expand them to make their denominators the same. Multiply 3x^{3}-9x^{2}+3x+7 times \frac{4}{4}.

$$\frac{x^{3}-64}{4}+\frac{4\left(3x^{3}-9x^{2}+3x+7\right)}{4}$$

Since \frac{x^{3}-64}{4} and \frac{4\left(3x^{3}-9x^{2}+3x+7\right)}{4} have the same denominator, add them by adding their numerators.

$$\frac{x^{3}-64+4\left(3x^{3}-9x^{2}+3x+7\right)}{4}$$

Do the multiplications in x^{3}-64+4\left(3x^{3}-9x^{2}+3x+7\right).

$$\frac{x^{3}-64+12x^{3}-36x^{2}+12x+28}{4}$$

Combine like terms in x^{3}-64+12x^{3}-36x^{2}+12x+28.

$$\frac{13x^{3}-36-36x^{2}+12x}{4}$$

Expand

$$\frac{13x^{3}}{4}-9x^{2}+3x-9$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Multiply x+4 times \frac{4}{4}.

$$\left(x-4\right)\left(\frac{x^{2}}{4}+\frac{4\left(x+4\right)}{4}\right)+3\left(x^{2}-x-1\right)\left(x-2\right)+1$$

Since \frac{x^{2}}{4} and \frac{4\left(x+4\right)}{4} have the same denominator, add them by adding their numerators.

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

Do the multiplications in x^{2}+4\left(x+4\right).

$$\left(x-4\right)\times \frac{x^{2}+4x+16}{4}+3\left(x^{2}-x-1\right)\left(x-2\right)+1$$

Express \left(x-4\right)\times \frac{x^{2}+4x+16}{4} as a single fraction.

$$\frac{\left(x-4\right)\left(x^{2}+4x+16\right)}{4}+3\left(x^{2}-x-1\right)\left(x-2\right)+1$$

Use the distributive property to multiply x-4 by x^{2}+4x+16 and combine like terms.

$$\frac{x^{3}-64}{4}+3\left(x^{2}-x-1\right)\left(x-2\right)+1$$

Use the distributive property to multiply 3 by x^{2}-x-1.

$$\frac{x^{3}-64}{4}+\left(3x^{2}-3x-3\right)\left(x-2\right)+1$$

Use the distributive property to multiply 3x^{2}-3x-3 by x-2 and combine like terms.

$$\frac{x^{3}-64}{4}+3x^{3}-9x^{2}+3x+6+1$$

Add 6 and 1 to get 7.

$$\frac{x^{3}-64}{4}+3x^{3}-9x^{2}+3x+7$$

To add or subtract expressions, expand them to make their denominators the same. Multiply 3x^{3}-9x^{2}+3x+7 times \frac{4}{4}.

$$\frac{x^{3}-64}{4}+\frac{4\left(3x^{3}-9x^{2}+3x+7\right)}{4}$$

Since \frac{x^{3}-64}{4} and \frac{4\left(3x^{3}-9x^{2}+3x+7\right)}{4} have the same denominator, add them by adding their numerators.

$$\frac{x^{3}-64+4\left(3x^{3}-9x^{2}+3x+7\right)}{4}$$

Do the multiplications in x^{3}-64+4\left(3x^{3}-9x^{2}+3x+7\right).

$$\frac{x^{3}-64+12x^{3}-36x^{2}+12x+28}{4}$$

Combine like terms in x^{3}-64+12x^{3}-36x^{2}+12x+28.

$$\frac{13x^{3}-36-36x^{2}+12x}{4}$$