Solve (x/2-3)(x/2+3)

$$( \frac { x } { 2 } - 3 ) ( \frac { x } { 2 } + 3 )$$

Evaluate

$$\frac{x^{2}}{4}-9$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Multiply 3 times \frac{2}{2}.

$$\left(\frac{x}{2}-\frac{3\times 2}{2}\right)\left(\frac{x}{2}+3\right)$$

Since \frac{x}{2} and \frac{3\times 2}{2} have the same denominator, subtract them by subtracting their numerators.

$$\frac{x-3\times 2}{2}\left(\frac{x}{2}+3\right)$$

Do the multiplications in x-3\times 2.

$$\frac{x-6}{2}\left(\frac{x}{2}+3\right)$$

To add or subtract expressions, expand them to make their denominators the same. Multiply 3 times \frac{2}{2}.

$$\frac{x-6}{2}\left(\frac{x}{2}+\frac{3\times 2}{2}\right)$$

Since \frac{x}{2} and \frac{3\times 2}{2} have the same denominator, add them by adding their numerators.

$$\frac{x-6}{2}\times \frac{x+3\times 2}{2}$$

Do the multiplications in x+3\times 2.

$$\frac{x-6}{2}\times \frac{x+6}{2}$$

Multiply \frac{x-6}{2} times \frac{x+6}{2} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\left(x-6\right)\left(x+6\right)}{2\times 2}$$

Multiply 2 and 2 to get 4.

$$\frac{\left(x-6\right)\left(x+6\right)}{4}$$

Consider \left(x-6\right)\left(x+6\right). Multiplication can be transformed into difference of squares using the rule: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}.

$$\frac{x^{2}-6^{2}}{4}$$

Calculate 6 to the power of 2 and get 36.

$$\frac{x^{2}-36}{4}$$

Expand

$$\frac{x^{2}}{4}-9$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Multiply 3 times \frac{2}{2}.

$$\left(\frac{x}{2}-\frac{3\times 2}{2}\right)\left(\frac{x}{2}+3\right)$$

Since \frac{x}{2} and \frac{3\times 2}{2} have the same denominator, subtract them by subtracting their numerators.

$$\frac{x-3\times 2}{2}\left(\frac{x}{2}+3\right)$$

Do the multiplications in x-3\times 2.

$$\frac{x-6}{2}\left(\frac{x}{2}+3\right)$$

To add or subtract expressions, expand them to make their denominators the same. Multiply 3 times \frac{2}{2}.

$$\frac{x-6}{2}\left(\frac{x}{2}+\frac{3\times 2}{2}\right)$$

Since \frac{x}{2} and \frac{3\times 2}{2} have the same denominator, add them by adding their numerators.

$$\frac{x-6}{2}\times \frac{x+3\times 2}{2}$$

Do the multiplications in x+3\times 2.

$$\frac{x-6}{2}\times \frac{x+6}{2}$$

Multiply \frac{x-6}{2} times \frac{x+6}{2} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\left(x-6\right)\left(x+6\right)}{2\times 2}$$

Multiply 2 and 2 to get 4.

$$\frac{\left(x-6\right)\left(x+6\right)}{4}$$

Consider \left(x-6\right)\left(x+6\right). Multiplication can be transformed into difference of squares using the rule: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}.

$$\frac{x^{2}-6^{2}}{4}$$

Calculate 6 to the power of 2 and get 36.

$$\frac{x^{2}-36}{4}$$