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

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

Evaluate

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

Solution Steps

Use the distributive property to multiply x by x+1.

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

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

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

Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(x+1\right)^{2}.

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

To find the opposite of x^{2}+2x+1, find the opposite of each term.

$$x^{3}-x^{2}-2x-x^{2}-2x-1$$

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

$$x^{3}-2x^{2}-2x-2x-1$$

Combine -2x and -2x to get -4x.

$$x^{3}-2x^{2}-4x-1$$

Expand

$$x^{3}-2x^{2}-4x-1$$

Solution Steps

Use the distributive property to multiply x by x+1.

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

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

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

Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(x+1\right)^{2}.

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

To find the opposite of x^{2}+2x+1, find the opposite of each term.

$$x^{3}-x^{2}-2x-x^{2}-2x-1$$

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

$$x^{3}-2x^{2}-2x-2x-1$$

Combine -2x and -2x to get -4x.

$$x^{3}-2x^{2}-4x-1$$