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

This article will guide you through simplifying the given algebraic expression: **(a+b)(c-d)+(a-b)(c+d)+2(ac+bd)**. We'll use the distributive property and some algebraic manipulation to arrive at the simplified form.

### Expanding the Expressions

Let's start by expanding the first two terms using the distributive property (also known as FOIL):

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

Now, let's substitute these expanded forms back into the original expression:

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

### Combining Like Terms

Next, we combine the like terms:

**ac + ac + 2ac = 4ac****-ad + ad = 0****bc - bc = 0****-bd - bd + 2bd = 0**

### Simplified Form

After combining the terms, we are left with:

**4ac**

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