Solve 2x^3+1/4x*1/2x^2-(3/2x)^3

$$2 x ^ { 3 } + \frac { 1 } { 4 } x \times \frac { 1 } { 2 } x ^ { 2 } - ( \frac { 3 } { 2 } x ) ^ { 3 }$$

Evaluate

$$-\frac{5x^{3}}{4}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 1 and 2 to get 3.

$$2x^{3}+\frac{1}{4}x^{3}\times \frac{1}{2}-\left(\frac{3}{2}x\right)^{3}$$

Multiply \frac{1}{4} and \frac{1}{2} to get \frac{1}{8}.

$$2x^{3}+\frac{1}{8}x^{3}-\left(\frac{3}{2}x\right)^{3}$$

Combine 2x^{3} and \frac{1}{8}x^{3} to get \frac{17}{8}x^{3}.

$$\frac{17}{8}x^{3}-\left(\frac{3}{2}x\right)^{3}$$

Expand \left(\frac{3}{2}x\right)^{3}.

$$\frac{17}{8}x^{3}-\left(\frac{3}{2}\right)^{3}x^{3}$$

Calculate \frac{3}{2} to the power of 3 and get \frac{27}{8}.

$$\frac{17}{8}x^{3}-\frac{27}{8}x^{3}$$

Combine \frac{17}{8}x^{3} and -\frac{27}{8}x^{3} to get -\frac{5}{4}x^{3}.

$$-\frac{5}{4}x^{3}$$

Expand

$$-\frac{5x^{3}}{4}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 1 and 2 to get 3.

$$2x^{3}+\frac{1}{4}x^{3}\times \frac{1}{2}-\left(\frac{3}{2}x\right)^{3}$$

Multiply \frac{1}{4} and \frac{1}{2} to get \frac{1}{8}.

$$2x^{3}+\frac{1}{8}x^{3}-\left(\frac{3}{2}x\right)^{3}$$

Combine 2x^{3} and \frac{1}{8}x^{3} to get \frac{17}{8}x^{3}.

$$\frac{17}{8}x^{3}-\left(\frac{3}{2}x\right)^{3}$$

Expand \left(\frac{3}{2}x\right)^{3}.

$$\frac{17}{8}x^{3}-\left(\frac{3}{2}\right)^{3}x^{3}$$

Calculate \frac{3}{2} to the power of 3 and get \frac{27}{8}.

$$\frac{17}{8}x^{3}-\frac{27}{8}x^{3}$$

Combine \frac{17}{8}x^{3} and -\frac{27}{8}x^{3} to get -\frac{5}{4}x^{3}.

$$-\frac{5}{4}x^{3}$$