## Simplifying the Expression (a+b)(c-d)+(a-b)(c+d)+2(ac+bd)

This article will guide you through the process of simplifying the algebraic expression: **(a+b)(c-d)+(a-b)(c+d)+2(ac+bd)**.

### Step 1: Expanding the Products

We begin by expanding the products using the **FOIL** (First, Outer, Inner, Last) method:

**(a+b)(c-d)**= ac - ad + bc - bd**(a-b)(c+d)**= ac + ad - bc - bd

### Step 2: Combining Like Terms

Now, let's substitute these expanded terms back into the original expression and combine the like terms:

**(ac - ad + bc - bd) + (ac + ad - bc - bd) + 2(ac + bd)**

= ac - ad + bc - bd + ac + ad - bc - bd + 2ac + 2bd

= **4ac**

### Simplified Expression

After combining all the terms, we are left with the simplified expression: **4ac**.

Therefore, the simplified form of the expression (a+b)(c-d)+(a-b)(c+d)+2(ac+bd) is **4ac**.