Solve (a+b)(c-d)+(a-b)(c+d)+2(ac+bd)

$$( a + b ) ( c - d ) + ( a - b ) ( c + d ) + 2 ( a c + b d )$$

Evaluate

$$4ac$$

Solution Steps

Apply the distributive property by multiplying each term of a+b by each term of c-d.

$$ac-ad+bc-bd+\left(a-b\right)\left(c+d\right)+2\left(ac+bd\right)$$

Apply the distributive property by multiplying each term of a-b by each term of c+d.

$$ac-ad+bc-bd+ac+ad-bc-bd+2\left(ac+bd\right)$$

Combine ac and ac to get 2ac.

$$2ac-ad+bc-bd+ad-bc-bd+2\left(ac+bd\right)$$

Combine -ad and ad to get 0.

$$2ac+bc-bd-bc-bd+2\left(ac+bd\right)$$

Combine bc and -bc to get 0.

$$2ac-bd-bd+2\left(ac+bd\right)$$

Combine -bd and -bd to get -2bd.

$$2ac-2bd+2\left(ac+bd\right)$$

Use the distributive property to multiply 2 by ac+bd.

$$2ac-2bd+2ac+2bd$$

Combine 2ac and 2ac to get 4ac.

$$4ac-2bd+2bd$$

Combine -2bd and 2bd to get 0.

$$4ac$$

Expand

$$4ac$$

Solution Steps

Apply the distributive property by multiplying each term of a+b by each term of c-d.

$$ac-ad+bc-bd+\left(a-b\right)\left(c+d\right)+2\left(ac+bd\right)$$

Apply the distributive property by multiplying each term of a-b by each term of c+d.

$$ac-ad+bc-bd+ac+ad-bc-bd+2\left(ac+bd\right)$$

Combine ac and ac to get 2ac.

$$2ac-ad+bc-bd+ad-bc-bd+2\left(ac+bd\right)$$

Combine -ad and ad to get 0.

$$2ac+bc-bd-bc-bd+2\left(ac+bd\right)$$

Combine bc and -bc to get 0.

$$2ac-bd-bd+2\left(ac+bd\right)$$

Combine -bd and -bd to get -2bd.

$$2ac-2bd+2\left(ac+bd\right)$$

Use the distributive property to multiply 2 by ac+bd.

$$2ac-2bd+2ac+2bd$$

Combine 2ac and 2ac to get 4ac.

$$4ac-2bd+2bd$$

Combine -2bd and 2bd to get 0.

$$4ac$$