Solve left(x/2+2right)left(x/2+4right)

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

Evaluate

$$\frac{\left(x+4\right)\left(x+8\right)}{4}$$

Short Solution Steps

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

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

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

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

Do the multiplications in x+2\times 2.

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

To add or subtract expressions, expand them to make their denominators the same. Multiply 4 times \frac{2}{2}.

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

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

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

Do the multiplications in x+4\times 2.

$$\frac{x+4}{2}\times \frac{x+8}{2}$$

Multiply \frac{x+4}{2} times \frac{x+8}{2} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\left(x+4\right)\left(x+8\right)}{2\times 2}$$

Multiply 2 and 2 to get 4.

$$\frac{\left(x+4\right)\left(x+8\right)}{4}$$

Apply the distributive property by multiplying each term of x+4 by each term of x+8.

$$\frac{x^{2}+8x+4x+32}{4}$$

Combine 8x and 4x to get 12x.

$$\frac{x^{2}+12x+32}{4}$$

Expand

$$\frac{x^{2}}{4}+3x+8$$

Short Solution Steps

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

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

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

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

Do the multiplications in x+2\times 2.

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

To add or subtract expressions, expand them to make their denominators the same. Multiply 4 times \frac{2}{2}.

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

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

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

Do the multiplications in x+4\times 2.

$$\frac{x+4}{2}\times \frac{x+8}{2}$$

Multiply \frac{x+4}{2} times \frac{x+8}{2} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\left(x+4\right)\left(x+8\right)}{2\times 2}$$

Multiply 2 and 2 to get 4.

$$\frac{\left(x+4\right)\left(x+8\right)}{4}$$

Apply the distributive property by multiplying each term of x+4 by each term of x+8.

$$\frac{x^{2}+8x+4x+32}{4}$$

Combine 8x and 4x to get 12x.

$$\frac{x^{2}+12x+32}{4}$$