(a+b)(c+d) Simplify

Jasonbradley

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Jun 16, 2024

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Simplifying (a+b)(c+d)

The expression (a+b)(c+d) is a product of two binomials. To simplify it, we can use the distributive property of multiplication.

Here's how it works:

1. Expand the first binomial: Think of (a+b) as a single entity and multiply it by each term inside the second binomial (c+d).

   (a+b)(c+d) = (a+b) * c + (a+b) * d

2. Apply the distributive property again: Now distribute the 'c' and 'd' to the terms inside the parentheses.

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

Therefore, the simplified form of (a+b)(c+d) is ac + bc + ad + bd.

Understanding the Concept

This method is essentially a visual representation of the FOIL method, which stands for First, Outer, Inner, Last.

• First: a * c
• Outer: a * d
• Inner: b * c
• Last: b * d

Remember, FOIL is simply a mnemonic device for remembering the steps of the distributive property when multiplying two binomials.

Example

Let's say we have the expression (x + 2)(y + 3). Using the distributive property (or FOIL):

1. First: x * y = xy
2. Outer: x * 3 = 3x
3. Inner: 2 * y = 2y
4. Last: 2 * 3 = 6

Combining the terms, we get: xy + 3x + 2y + 6

Conclusion

Simplifying (a+b)(c+d) using the distributive property is a fundamental concept in algebra. Understanding this process is crucial for working with polynomials and solving algebraic equations.