Solve left(x-3right)left(x^2+3x+9right)-xleft(x-3right)left(x+3right)+9left(3-xright)+1

$$\left( x-3 \right) \left( { x }^{ 2 } +3x+9 \right) -x \left( x-3 \right) \left( x+3 \right) +9 \left( 3-x \right) +1$$

Evaluate

$$1$$

Solution Steps

Use the distributive property to multiply x-3 by x^{2}+3x+9 and combine like terms.

$$x^{3}-27-x\left(x-3\right)\left(x+3\right)+9\left(3-x\right)+1$$

Use the distributive property to multiply x by x-3.

$$x^{3}-27-\left(x^{2}-3x\right)\left(x+3\right)+9\left(3-x\right)+1$$

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

$$x^{3}-27-\left(x^{3}-9x\right)+9\left(3-x\right)+1$$

To find the opposite of x^{3}-9x, find the opposite of each term.

$$x^{3}-27-x^{3}+9x+9\left(3-x\right)+1$$

Combine x^{3} and -x^{3} to get 0.

$$-27+9x+9\left(3-x\right)+1$$

Use the distributive property to multiply 9 by 3-x.

$$-27+9x+27-9x+1$$

Add -27 and 27 to get 0.

$$9x-9x+1$$

Combine 9x and -9x to get 0.

$$1$$

Factor

$$1$$