Solve (a-4)(a-2)-(a-1)(a-3)

$$( a - 4 ) ( a - 2 ) - ( a - 1 ) ( a - 3 )$$

Evaluate

$$5-2a$$

Solution Steps

Apply the distributive property by multiplying each term of a-4 by each term of a-2.

$$a^{2}-2a-4a+8-\left(a-1\right)\left(a-3\right)$$

Combine -2a and -4a to get -6a.

$$a^{2}-6a+8-\left(a-1\right)\left(a-3\right)$$

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

$$a^{2}-6a+8-\left(a^{2}-3a-a+3\right)$$

Combine -3a and -a to get -4a.

$$a^{2}-6a+8-\left(a^{2}-4a+3\right)$$

To find the opposite of a^{2}-4a+3, find the opposite of each term.

$$a^{2}-6a+8-a^{2}-\left(-4a\right)-3$$

The opposite of -4a is 4a.

$$a^{2}-6a+8-a^{2}+4a-3$$

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

$$-6a+8+4a-3$$

Combine -6a and 4a to get -2a.

$$-2a+8-3$$

Subtract 3 from 8 to get 5.

$$-2a+5$$

Expand

$$5-2a$$

Solution Steps

Apply the distributive property by multiplying each term of a-4 by each term of a-2.

$$a^{2}-2a-4a+8-\left(a-1\right)\left(a-3\right)$$

Combine -2a and -4a to get -6a.

$$a^{2}-6a+8-\left(a-1\right)\left(a-3\right)$$

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

$$a^{2}-6a+8-\left(a^{2}-3a-a+3\right)$$

Combine -3a and -a to get -4a.

$$a^{2}-6a+8-\left(a^{2}-4a+3\right)$$

To find the opposite of a^{2}-4a+3, find the opposite of each term.

$$a^{2}-6a+8-a^{2}-\left(-4a\right)-3$$

The opposite of -4a is 4a.

$$a^{2}-6a+8-a^{2}+4a-3$$

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

$$-6a+8+4a-3$$

Combine -6a and 4a to get -2a.

$$-2a+8-3$$

Subtract 3 from 8 to get 5.

$$-2a+5$$