(a+b)(c+d) Answer

Jasonbradley

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Jun 16, 2024

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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:

1. First: Multiply the first terms of each binomial: a * c = ac
2. Outer: Multiply the outer terms of the binomials: a * d = ad
3. Inner: Multiply the inner terms of the binomials: b * c = bc
4. 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):

1. a(c+d) = ac + ad
2. 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.