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

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

Evaluate

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

Short Solution Steps

Use the distributive property to multiply 3x^{2}-4 by x-2.

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

Use the distributive property to multiply x^{2}-4x+1 by x.

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

To find the opposite of x^{3}-4x^{2}+x, find the opposite of each term.

$$\frac{3x^{3}-6x^{2}-4x+8-x^{3}+4x^{2}-x}{x^{2}-4x+4}$$

Combine 3x^{3} and -x^{3} to get 2x^{3}.

$$\frac{2x^{3}-6x^{2}-4x+8+4x^{2}-x}{x^{2}-4x+4}$$

Combine -6x^{2} and 4x^{2} to get -2x^{2}.

$$\frac{2x^{3}-2x^{2}-4x+8-x}{x^{2}-4x+4}$$

Combine -4x and -x to get -5x.

$$\frac{2x^{3}-2x^{2}-5x+8}{x^{2}-4x+4}$$

Expand

$$\frac{2x^{3}-2x^{2}-5x+8}{x^{2}-4x+4}$$

Short Solution Steps

Use the distributive property to multiply 3x^{2}-4 by x-2.

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

Use the distributive property to multiply x^{2}-4x+1 by x.

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

To find the opposite of x^{3}-4x^{2}+x, find the opposite of each term.

$$\frac{3x^{3}-6x^{2}-4x+8-x^{3}+4x^{2}-x}{x^{2}-4x+4}$$

Combine 3x^{3} and -x^{3} to get 2x^{3}.

$$\frac{2x^{3}-6x^{2}-4x+8+4x^{2}-x}{x^{2}-4x+4}$$

Combine -6x^{2} and 4x^{2} to get -2x^{2}.

$$\frac{2x^{3}-2x^{2}-4x+8-x}{x^{2}-4x+4}$$

Combine -4x and -x to get -5x.

$$\frac{2x^{3}-2x^{2}-5x+8}{x^{2}-4x+4}$$