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

$$x(x+1)-(x-1)(x-2)$$

Evaluate

$$4x-2$$

Solution Steps

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

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

Apply the distributive property by multiplying each term of x-1 by each term of x-2.

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

Combine -2x and -x to get -3x.

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

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

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

The opposite of -3x is 3x.

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

Combine x^{2} and -x^{2} to get 0.

$$x+3x-2$$

Combine x and 3x to get 4x.

$$4x-2$$

Expand

$$4x-2$$

Solution Steps

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

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

Apply the distributive property by multiplying each term of x-1 by each term of x-2.

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

Combine -2x and -x to get -3x.

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

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

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

The opposite of -3x is 3x.

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

Combine x^{2} and -x^{2} to get 0.

$$x+3x-2$$

Combine x and 3x to get 4x.

$$4x-2$$