Solve (x-1)(x+1)-x(x-3)

$$( x - 1 ) ( x + 1 ) - x ( x - 3 )$$

Evaluate

$$3x-1$$

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}.

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

Calculate 1 to the power of 2 and get 1.

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

Use the distributive property to multiply x by x-3.

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

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

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

The opposite of -3x is 3x.

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

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

$$-1+3x$$

Expand

$$3x-1$$

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}.

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

Calculate 1 to the power of 2 and get 1.

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

Use the distributive property to multiply x by x-3.

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

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

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

The opposite of -3x is 3x.

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

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

$$-1+3x$$