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

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 expression might look daunting at first, but we can simplify it using the distributive property and combining like terms. Here's how:

1. Expanding the Parentheses

First, we expand each of the products using the distributive property (also known as FOIL).

• (a+b)(c-d):

  • ac - ad + bc - bd

• (a-b)(c+d):

  • ac + ad - bc - bd

• 2(ac + bd):

  • 2ac + 2bd

2. Combining Like Terms

Now we have:

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

Let's group the like terms:

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

Simplifying this gives us:

4ac

Final Result

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