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

Jasonbradley

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Jun 16, 2024

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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.