Solve ((x*(x+2)(2x+1))div8)-(x*(x+1))div2=

$$((x \times (x+2)(2x+1)) \div 8)-(x \times (x+1)) \div 2=$$

Evaluate

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

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 8 and 2 is 8. Multiply \frac{x\left(x+1\right)}{2} times \frac{4}{4}.

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

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

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

Do the multiplications in x\left(x+2\right)\left(2x+1\right)-4x\left(x+1\right).

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

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

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

Expand

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

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 8 and 2 is 8. Multiply \frac{x\left(x+1\right)}{2} times \frac{4}{4}.

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

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

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

Do the multiplications in x\left(x+2\right)\left(2x+1\right)-4x\left(x+1\right).

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

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

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