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

$$( x - \frac { 1 } { 2 } ) - ( a - \frac { 2 } { 2 } ) ( a + \frac { 2 } { 2 } )$$

Evaluate

$$x-a^{2}+\frac{1}{2}$$

Solution Steps

Divide 2 by 2 to get 1.

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

Divide 2 by 2 to get 1.

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

Consider \left(a-1\right)\left(a+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}.

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

Calculate 1 to the power of 2 and get 1.

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

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

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

The opposite of -1 is 1.

$$x-\frac{1}{2}-a^{2}+1$$

Convert 1 to fraction \frac{2}{2}.

$$x-\frac{1}{2}-a^{2}+\frac{2}{2}$$

Since -\frac{1}{2} and \frac{2}{2} have the same denominator, add them by adding their numerators.

$$x+\frac{-1+2}{2}-a^{2}$$

Add -1 and 2 to get 1.

$$x+\frac{1}{2}-a^{2}$$

Expand

$$x-a^{2}+\frac{1}{2}$$

Solution Steps

Divide 2 by 2 to get 1.

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

Divide 2 by 2 to get 1.

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

Consider \left(a-1\right)\left(a+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}.

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

Calculate 1 to the power of 2 and get 1.

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

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

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

The opposite of -1 is 1.

$$x-\frac{1}{2}-a^{2}+1$$

Convert 1 to fraction \frac{2}{2}.

$$x-\frac{1}{2}-a^{2}+\frac{2}{2}$$

Since -\frac{1}{2} and \frac{2}{2} have the same denominator, add them by adding their numerators.

$$x+\frac{-1+2}{2}-a^{2}$$

Add -1 and 2 to get 1.

$$x+\frac{1}{2}-a^{2}$$