Solve 2n^2+n-2left(n-1right)^2-n+1

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

Evaluate

$$4n-1$$

Solution Steps

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

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

Use the distributive property to multiply -2 by n^{2}-2n+1.

$$2n^{2}+n-2n^{2}+4n-2-n+1$$

Combine 2n^{2} and -2n^{2} to get 0.

$$n+4n-2-n+1$$

Combine n and 4n to get 5n.

$$5n-2-n+1$$

Combine 5n and -n to get 4n.

$$4n-2+1$$

Add -2 and 1 to get -1.

$$4n-1$$

Expand

$$4n-1$$

Solution Steps

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

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

Use the distributive property to multiply -2 by n^{2}-2n+1.

$$2n^{2}+n-2n^{2}+4n-2-n+1$$

Combine 2n^{2} and -2n^{2} to get 0.

$$n+4n-2-n+1$$

Combine n and 4n to get 5n.

$$5n-2-n+1$$

Combine 5n and -n to get 4n.

$$4n-2+1$$

Add -2 and 1 to get -1.

$$4n-1$$