Solve n(2018n-1)-(n-1)[2018(n-1)-1]

$$n ( 2018 n - 1 ) - ( n - 1 ) [ 2018 ( n - 1 ) - 1 ]$$

Evaluate

$$4036n-2019$$

Solution Steps

Use the distributive property to multiply n by 2018n-1.

$$2018n^{2}-n-\left(n-1\right)\left(2018\left(n-1\right)-1\right)$$

Use the distributive property to multiply 2018 by n-1.

$$2018n^{2}-n-\left(n-1\right)\left(2018n-2018-1\right)$$

Subtract 1 from -2018 to get -2019.

$$2018n^{2}-n-\left(n-1\right)\left(2018n-2019\right)$$

Apply the distributive property by multiplying each term of n-1 by each term of 2018n-2019.

$$2018n^{2}-n-\left(2018n^{2}-2019n-2018n+2019\right)$$

Combine -2019n and -2018n to get -4037n.

$$2018n^{2}-n-\left(2018n^{2}-4037n+2019\right)$$

To find the opposite of 2018n^{2}-4037n+2019, find the opposite of each term.

$$2018n^{2}-n-2018n^{2}-\left(-4037n\right)-2019$$

The opposite of -4037n is 4037n.

$$2018n^{2}-n-2018n^{2}+4037n-2019$$

Combine 2018n^{2} and -2018n^{2} to get 0.

$$-n+4037n-2019$$

Combine -n and 4037n to get 4036n.

$$4036n-2019$$

Expand

$$4036n-2019$$

Solution Steps

Use the distributive property to multiply n by 2018n-1.

$$2018n^{2}-n-\left(n-1\right)\left(2018\left(n-1\right)-1\right)$$

Use the distributive property to multiply 2018 by n-1.

$$2018n^{2}-n-\left(n-1\right)\left(2018n-2018-1\right)$$

Subtract 1 from -2018 to get -2019.

$$2018n^{2}-n-\left(n-1\right)\left(2018n-2019\right)$$

Apply the distributive property by multiplying each term of n-1 by each term of 2018n-2019.

$$2018n^{2}-n-\left(2018n^{2}-2019n-2018n+2019\right)$$

Combine -2019n and -2018n to get -4037n.

$$2018n^{2}-n-\left(2018n^{2}-4037n+2019\right)$$

To find the opposite of 2018n^{2}-4037n+2019, find the opposite of each term.

$$2018n^{2}-n-2018n^{2}-\left(-4037n\right)-2019$$

The opposite of -4037n is 4037n.

$$2018n^{2}-n-2018n^{2}+4037n-2019$$

Combine 2018n^{2} and -2018n^{2} to get 0.

$$-n+4037n-2019$$

Combine -n and 4037n to get 4036n.

$$4036n-2019$$