## Expanding (a+b)(c+d): A Guide to FOIL and Distributive Property

The expression **(a+b)(c+d)** is a common algebraic expression that often arises in various mathematical contexts. Expanding this expression involves multiplying out the terms within the parentheses, and there are two primary methods for doing so: **FOIL** and the **Distributive Property**.

### The FOIL Method

FOIL stands for **First, Outer, Inner, Last**. It's a mnemonic device for remembering the steps involved in multiplying binomials:

**First:**Multiply the**first**terms of each binomial:**a * c = ac****Outer:**Multiply the**outer**terms of the binomials:**a * d = ad****Inner:**Multiply the**inner**terms of the binomials:**b * c = bc****Last:**Multiply the**last**terms of each binomial:**b * d = bd**

Finally, add up all the resulting terms to get the expanded form: **ac + ad + bc + bd**.

### The Distributive Property

The distributive property is a more general approach that applies to multiplying any number of terms. It states that: **a(b+c) = ab + ac**.

Applying this to our expression, we distribute the first binomial (a+b) over the terms of the second binomial (c+d):

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

Then, we add the two results together: **ac + ad + bc + bd**.

### Summary

Both the FOIL method and the Distributive Property lead to the same expanded form: **ac + ad + bc + bd**. While FOIL provides a specific order to remember, the Distributive Property offers a more general and flexible approach for expanding expressions. Ultimately, the choice depends on personal preference and the complexity of the problem.