Solve (x-1/5)^3-2

$$( \frac { x - 1 } { 5 } ) ^ { 3 } - 2$$

Evaluate

$$\frac{\left(x-1\right)^{3}}{125}-2$$

Short Solution Steps

To raise \frac{x-1}{5} to a power, raise both numerator and denominator to the power and then divide.

$$\frac{\left(x-1\right)^{3}}{5^{3}}-2$$

To add or subtract expressions, expand them to make their denominators the same. Multiply 2 times \frac{5^{3}}{5^{3}}.

$$\frac{\left(x-1\right)^{3}}{5^{3}}-\frac{2\times 5^{3}}{5^{3}}$$

Since \frac{\left(x-1\right)^{3}}{5^{3}} and \frac{2\times 5^{3}}{5^{3}} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\left(x-1\right)^{3}-2\times 5^{3}}{5^{3}}$$

Do the multiplications in \left(x-1\right)^{3}-2\times 5^{3}.

$$\frac{x^{3}+3x^{2}\left(-1\right)+3x-1-250}{5^{3}}$$

Combine like terms in x^{3}+3x^{2}\left(-1\right)+3x-1-250.

$$\frac{x^{3}-3x^{2}+3x-251}{5^{3}}$$

Expand 5^{3}.

$$\frac{x^{3}-3x^{2}+3x-251}{125}$$

Expand

$$\frac{x^{3}-3x^{2}+3x-251}{125}$$

Short Solution Steps

To raise \frac{x-1}{5} to a power, raise both numerator and denominator to the power and then divide.

$$\frac{\left(x-1\right)^{3}}{5^{3}}-2$$

To add or subtract expressions, expand them to make their denominators the same. Multiply 2 times \frac{5^{3}}{5^{3}}.

$$\frac{\left(x-1\right)^{3}}{5^{3}}-\frac{2\times 5^{3}}{5^{3}}$$

Since \frac{\left(x-1\right)^{3}}{5^{3}} and \frac{2\times 5^{3}}{5^{3}} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\left(x-1\right)^{3}-2\times 5^{3}}{5^{3}}$$

Do the multiplications in \left(x-1\right)^{3}-2\times 5^{3}.

$$\frac{x^{3}+3x^{2}\left(-1\right)+3x-1-250}{5^{3}}$$

Combine like terms in x^{3}+3x^{2}\left(-1\right)+3x-1-250.

$$\frac{x^{3}-3x^{2}+3x-251}{5^{3}}$$

Expand 5^{3}.

$$\frac{x^{3}-3x^{2}+3x-251}{125}$$