Solve n^3-(n-1)^3

$$n ^ { 3 } - ( n - 1 ) ^ { 3 }$$

Evaluate

$$3n^{2}-3n+1$$

Solution Steps

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

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

To find the opposite of n^{3}-3n^{2}+3n-1, find the opposite of each term.

$$n^{3}-n^{3}+3n^{2}-3n+1$$

Combine n^{3} and -n^{3} to get 0.

$$3n^{2}-3n+1$$

Expand

$$3n^{2}-3n+1$$

Solution Steps

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

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

To find the opposite of n^{3}-3n^{2}+3n-1, find the opposite of each term.

$$n^{3}-n^{3}+3n^{2}-3n+1$$

Combine n^{3} and -n^{3} to get 0.

$$3n^{2}-3n+1$$