Solve (x/4+1/2)(x/4-1/2)

$$( \frac { x } { 4 } + \frac { 1 } { 2 } ) ( \frac { x } { 4 } - \frac { 1 } { 2 } )$$

Evaluate

$$\frac{x^{2}-4}{16}$$

Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 4 and 2 is 4. Multiply \frac{1}{2} times \frac{2}{2}.

$$\left(\frac{x}{4}+\frac{2}{4}\right)\left(\frac{x}{4}-\frac{1}{2}\right)$$

Since \frac{x}{4} and \frac{2}{4} have the same denominator, add them by adding their numerators.

$$\frac{x+2}{4}\left(\frac{x}{4}-\frac{1}{2}\right)$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 4 and 2 is 4. Multiply \frac{1}{2} times \frac{2}{2}.

$$\frac{x+2}{4}\left(\frac{x}{4}-\frac{2}{4}\right)$$

Since \frac{x}{4} and \frac{2}{4} have the same denominator, subtract them by subtracting their numerators.

$$\frac{x+2}{4}\times \frac{x-2}{4}$$

Multiply \frac{x+2}{4} times \frac{x-2}{4} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\left(x+2\right)\left(x-2\right)}{4\times 4}$$

Multiply 4 and 4 to get 16.

$$\frac{\left(x+2\right)\left(x-2\right)}{16}$$

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

$$\frac{x^{2}-2^{2}}{16}$$

Calculate 2 to the power of 2 and get 4.

$$\frac{x^{2}-4}{16}$$

Expand

$$\frac{x^{2}}{16}-\frac{1}{4}$$

Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 4 and 2 is 4. Multiply \frac{1}{2} times \frac{2}{2}.

$$\left(\frac{x}{4}+\frac{2}{4}\right)\left(\frac{x}{4}-\frac{1}{2}\right)$$

Since \frac{x}{4} and \frac{2}{4} have the same denominator, add them by adding their numerators.

$$\frac{x+2}{4}\left(\frac{x}{4}-\frac{1}{2}\right)$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 4 and 2 is 4. Multiply \frac{1}{2} times \frac{2}{2}.

$$\frac{x+2}{4}\left(\frac{x}{4}-\frac{2}{4}\right)$$

Since \frac{x}{4} and \frac{2}{4} have the same denominator, subtract them by subtracting their numerators.

$$\frac{x+2}{4}\times \frac{x-2}{4}$$

Multiply \frac{x+2}{4} times \frac{x-2}{4} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\left(x+2\right)\left(x-2\right)}{4\times 4}$$

Multiply 4 and 4 to get 16.

$$\frac{\left(x+2\right)\left(x-2\right)}{16}$$

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

$$\frac{x^{2}-2^{2}}{16}$$

Calculate 2 to the power of 2 and get 4.

$$\frac{x^{2}-4}{16}$$