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

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

Evaluate

$$2x+1$$

Solution Steps

Use the distributive property to multiply x by x+2.

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

Consider \left(x-1\right)\left(x+1\right). Multiplication can be transformed into difference of squares using the rule: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}.

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

Calculate 1 to the power of 2 and get 1.

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

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

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

The opposite of -1 is 1.

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

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

$$2x+1$$

Expand

$$2x+1$$

Solution Steps

Use the distributive property to multiply x by x+2.

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

Consider \left(x-1\right)\left(x+1\right). Multiplication can be transformed into difference of squares using the rule: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}.

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

Calculate 1 to the power of 2 and get 1.

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

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

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

The opposite of -1 is 1.

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

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

$$2x+1$$