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

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

Evaluate

$$\frac{\left(x+8\right)\left(x+16\right)}{16}$$

Short Solution Steps

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

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

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

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

Do the multiplications in 2\times 4+x.

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

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

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

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

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

Do the multiplications in 4\times 4+x.

$$\frac{8+x}{4}\times \frac{16+x}{4}$$

Multiply \frac{8+x}{4} times \frac{16+x}{4} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\left(8+x\right)\left(16+x\right)}{4\times 4}$$

Multiply 4 and 4 to get 16.

$$\frac{\left(8+x\right)\left(16+x\right)}{16}$$

Apply the distributive property by multiplying each term of 8+x by each term of 16+x.

$$\frac{128+8x+16x+x^{2}}{16}$$

Combine 8x and 16x to get 24x.

$$\frac{128+24x+x^{2}}{16}$$

Expand

$$\frac{x^{2}}{16}+\frac{3x}{2}+8$$

Short Solution Steps

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

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

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

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

Do the multiplications in 2\times 4+x.

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

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

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

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

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

Do the multiplications in 4\times 4+x.

$$\frac{8+x}{4}\times \frac{16+x}{4}$$

Multiply \frac{8+x}{4} times \frac{16+x}{4} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\left(8+x\right)\left(16+x\right)}{4\times 4}$$

Multiply 4 and 4 to get 16.

$$\frac{\left(8+x\right)\left(16+x\right)}{16}$$

Apply the distributive property by multiplying each term of 8+x by each term of 16+x.

$$\frac{128+8x+16x+x^{2}}{16}$$

Combine 8x and 16x to get 24x.

$$\frac{128+24x+x^{2}}{16}$$