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

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

Evaluate

$$2\left(x-1\right)$$

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}. Square 1.

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

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

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

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

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

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

$$-1+2x-1$$

Subtract 1 from -1 to get -2.

$$-2+2x$$

Expand

$$2x-2$$

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}. Square 1.

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

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

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

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

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

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

$$-1+2x-1$$

Subtract 1 from -1 to get -2.

$$-2+2x$$