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

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 explore the process of simplifying the algebraic expression: (a+b)(c-d)+(a-b)(c+d)+2(ac+bd). We'll use the distributive property and basic algebraic operations to arrive at a more concise form.

Expanding the Expression

Let's begin by expanding the expression using the distributive property:

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

Substituting these expansions into the original expression, we get:

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

Combining Like Terms

Now, let's combine the like terms:

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

Simplified Expression

Finally, we have simplified the expression to:

(a+b)(c-d)+(a-b)(c+d)+2(ac+bd) = 4ac

Therefore, the simplified form of the given expression is 4ac.