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

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 the process of simplifying the algebraic expression: (a+b)(c-d)+(a-b)(c+d)+2(ac+bd).

Step 1: Expanding the Products

We begin by expanding the products using the FOIL (First, Outer, Inner, Last) method:

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

Step 2: Combining Like Terms

Now, let's substitute these expanded terms back into the original expression and combine the like terms:

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

= ac - ad + bc - bd + ac + ad - bc - bd + 2ac + 2bd

= 4ac

Simplified Expression

After combining all the terms, we are left with the simplified expression: 4ac.

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