Solve (5n-2)3n-(5n-2)(n-1)

$$( 5 n - 2 ) 3 n - ( 5 n - 2 ) ( n - 1 )$$

Evaluate

$$10n^{2}+n-2$$

Solution Steps

Use the distributive property to multiply 5n-2 by 3.

$$\left(15n-6\right)n-\left(5n-2\right)\left(n-1\right)$$

Use the distributive property to multiply 15n-6 by n.

$$15n^{2}-6n-\left(5n-2\right)\left(n-1\right)$$

Apply the distributive property by multiplying each term of 5n-2 by each term of n-1.

$$15n^{2}-6n-\left(5n^{2}-5n-2n+2\right)$$

Combine -5n and -2n to get -7n.

$$15n^{2}-6n-\left(5n^{2}-7n+2\right)$$

To find the opposite of 5n^{2}-7n+2, find the opposite of each term.

$$15n^{2}-6n-5n^{2}-\left(-7n\right)-2$$

The opposite of -7n is 7n.

$$15n^{2}-6n-5n^{2}+7n-2$$

Combine 15n^{2} and -5n^{2} to get 10n^{2}.

$$10n^{2}-6n+7n-2$$

Combine -6n and 7n to get n.

$$10n^{2}+n-2$$

Expand

$$10n^{2}+n-2$$

Solution Steps

Use the distributive property to multiply 5n-2 by 3.

$$\left(15n-6\right)n-\left(5n-2\right)\left(n-1\right)$$

Use the distributive property to multiply 15n-6 by n.

$$15n^{2}-6n-\left(5n-2\right)\left(n-1\right)$$

Apply the distributive property by multiplying each term of 5n-2 by each term of n-1.

$$15n^{2}-6n-\left(5n^{2}-5n-2n+2\right)$$

Combine -5n and -2n to get -7n.

$$15n^{2}-6n-\left(5n^{2}-7n+2\right)$$

To find the opposite of 5n^{2}-7n+2, find the opposite of each term.

$$15n^{2}-6n-5n^{2}-\left(-7n\right)-2$$

The opposite of -7n is 7n.

$$15n^{2}-6n-5n^{2}+7n-2$$

Combine 15n^{2} and -5n^{2} to get 10n^{2}.

$$10n^{2}-6n+7n-2$$

Combine -6n and 7n to get n.

$$10n^{2}+n-2$$