Solve (2a-1)(a+1)-(a-1)(2a-3)

$$( 2 a - 1 ) ( a + 1 ) - ( a - 1 ) ( 2 a - 3 )$$

Evaluate

$$6a-4$$

Solution Steps

Apply the distributive property by multiplying each term of 2a-1 by each term of a+1.

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

Combine 2a and -a to get a.

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

Apply the distributive property by multiplying each term of a-1 by each term of 2a-3.

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

Combine -3a and -2a to get -5a.

$$2a^{2}+a-1-\left(2a^{2}-5a+3\right)$$

To find the opposite of 2a^{2}-5a+3, find the opposite of each term.

$$2a^{2}+a-1-2a^{2}-\left(-5a\right)-3$$

The opposite of -5a is 5a.

$$2a^{2}+a-1-2a^{2}+5a-3$$

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

$$a-1+5a-3$$

Combine a and 5a to get 6a.

$$6a-1-3$$

Subtract 3 from -1 to get -4.

$$6a-4$$

Expand

$$6a-4$$

Solution Steps

Apply the distributive property by multiplying each term of 2a-1 by each term of a+1.

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

Combine 2a and -a to get a.

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

Apply the distributive property by multiplying each term of a-1 by each term of 2a-3.

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

Combine -3a and -2a to get -5a.

$$2a^{2}+a-1-\left(2a^{2}-5a+3\right)$$

To find the opposite of 2a^{2}-5a+3, find the opposite of each term.

$$2a^{2}+a-1-2a^{2}-\left(-5a\right)-3$$

The opposite of -5a is 5a.

$$2a^{2}+a-1-2a^{2}+5a-3$$

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

$$a-1+5a-3$$

Combine a and 5a to get 6a.

$$6a-1-3$$

Subtract 3 from -1 to get -4.

$$6a-4$$