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

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

Evaluate

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

Solution Steps

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}.

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

Calculate 1 to the power of 2 and get 1.

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

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

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

The opposite of -1 is 1.

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

Add 2 and 1 to get 3.

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

Expand

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

Solution Steps

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}.

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

Calculate 1 to the power of 2 and get 1.

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

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

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

The opposite of -1 is 1.

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

Add 2 and 1 to get 3.

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