Solve 1/3*(x-1)^3

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

Evaluate

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

Solution Steps

Use binomial theorem \left(a-b\right)^{3}=a^{3}-3a^{2}b+3ab^{2}-b^{3} to expand \left(x-1\right)^{3}.

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

Use the distributive property to multiply \frac{1}{3} by x^{3}-3x^{2}+3x-1.

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

Expand

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

Solution Steps

Use binomial theorem \left(a-b\right)^{3}=a^{3}-3a^{2}b+3ab^{2}-b^{3} to expand \left(x-1\right)^{3}.

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

Use the distributive property to multiply \frac{1}{3} by x^{3}-3x^{2}+3x-1.

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