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

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

Evaluate

$$1-9x$$

Solution Steps

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

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

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

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

Use the distributive property to multiply x-1 by x^{2}+x+1 and combine like terms.

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

To find the opposite of x^{3}-1, find the opposite of each term.

$$x^{3}-9x-x^{3}+1$$

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

$$-9x+1$$

Expand

$$1-9x$$

Solution Steps

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

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

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

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

Use the distributive property to multiply x-1 by x^{2}+x+1 and combine like terms.

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

To find the opposite of x^{3}-1, find the opposite of each term.

$$x^{3}-9x-x^{3}+1$$

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

$$-9x+1$$