Solve (2x+1)(x^2/2+x/4+1/8)+1/8

$$(2x+1)( \frac{ { x }^{ 2 } }{ 2 } + \frac{ x }{ 4 } + \frac{ 1 }{ 8 } )+ \frac{ 1 }{ 8 }$$

Evaluate

$$x^{3}+x^{2}+\frac{x}{2}+\frac{1}{4}$$

Short Solution Steps

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

$$\left(2x+1\right)\left(\frac{2x^{2}}{4}+\frac{x}{4}+\frac{1}{8}\right)+\frac{1}{8}$$

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

$$\left(2x+1\right)\left(\frac{2x^{2}+x}{4}+\frac{1}{8}\right)+\frac{1}{8}$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 4 and 8 is 8. Multiply \frac{2x^{2}+x}{4} times \frac{2}{2}.

$$\left(2x+1\right)\left(\frac{2\left(2x^{2}+x\right)}{8}+\frac{1}{8}\right)+\frac{1}{8}$$

Since \frac{2\left(2x^{2}+x\right)}{8} and \frac{1}{8} have the same denominator, add them by adding their numerators.

$$\left(2x+1\right)\times \frac{2\left(2x^{2}+x\right)+1}{8}+\frac{1}{8}$$

Do the multiplications in 2\left(2x^{2}+x\right)+1.

$$\left(2x+1\right)\times \frac{4x^{2}+2x+1}{8}+\frac{1}{8}$$

Express \left(2x+1\right)\times \frac{4x^{2}+2x+1}{8} as a single fraction.

$$\frac{\left(2x+1\right)\left(4x^{2}+2x+1\right)}{8}+\frac{1}{8}$$

Since \frac{\left(2x+1\right)\left(4x^{2}+2x+1\right)}{8} and \frac{1}{8} have the same denominator, add them by adding their numerators.

$$\frac{\left(2x+1\right)\left(4x^{2}+2x+1\right)+1}{8}$$

Do the multiplications in \left(2x+1\right)\left(4x^{2}+2x+1\right)+1.

$$\frac{8x^{3}+4x^{2}+2x+4x^{2}+2x+1+1}{8}$$

Combine like terms in 8x^{3}+4x^{2}+2x+4x^{2}+2x+1+1.

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

Expand

$$x^{3}+x^{2}+\frac{x}{2}+\frac{1}{4}$$

Short Solution Steps

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

$$\left(2x+1\right)\left(\frac{2x^{2}}{4}+\frac{x}{4}+\frac{1}{8}\right)+\frac{1}{8}$$

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

$$\left(2x+1\right)\left(\frac{2x^{2}+x}{4}+\frac{1}{8}\right)+\frac{1}{8}$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 4 and 8 is 8. Multiply \frac{2x^{2}+x}{4} times \frac{2}{2}.

$$\left(2x+1\right)\left(\frac{2\left(2x^{2}+x\right)}{8}+\frac{1}{8}\right)+\frac{1}{8}$$

Since \frac{2\left(2x^{2}+x\right)}{8} and \frac{1}{8} have the same denominator, add them by adding their numerators.

$$\left(2x+1\right)\times \frac{2\left(2x^{2}+x\right)+1}{8}+\frac{1}{8}$$

Do the multiplications in 2\left(2x^{2}+x\right)+1.

$$\left(2x+1\right)\times \frac{4x^{2}+2x+1}{8}+\frac{1}{8}$$

Express \left(2x+1\right)\times \frac{4x^{2}+2x+1}{8} as a single fraction.

$$\frac{\left(2x+1\right)\left(4x^{2}+2x+1\right)}{8}+\frac{1}{8}$$

Since \frac{\left(2x+1\right)\left(4x^{2}+2x+1\right)}{8} and \frac{1}{8} have the same denominator, add them by adding their numerators.

$$\frac{\left(2x+1\right)\left(4x^{2}+2x+1\right)+1}{8}$$

Do the multiplications in \left(2x+1\right)\left(4x^{2}+2x+1\right)+1.

$$\frac{8x^{3}+4x^{2}+2x+4x^{2}+2x+1+1}{8}$$

Combine like terms in 8x^{3}+4x^{2}+2x+4x^{2}+2x+1+1.

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