(a+b) X (c+d)

3 min read Jun 16, 2024
(a+b) X (c+d)

Expanding (a+b) x (c+d)

In mathematics, expanding expressions like (a+b) x (c+d) is a fundamental skill. It involves using the distributive property to simplify the expression and get rid of the parentheses. Here's how it works:

The Distributive Property

The distributive property states that multiplying a sum by a number is the same as multiplying each addend in the sum by the number and then adding the products. In other words:

a x (b + c) = (a x b) + (a x c)

Expanding (a+b) x (c+d)

To expand (a+b) x (c+d), we use the distributive property twice:

  1. First Distribution: Treat (c+d) as a single entity and distribute (a+b) over it: (a+b) x (c+d) = a x (c+d) + b x (c+d)

  2. Second Distribution: Now, distribute both 'a' and 'b' over (c+d): a x (c+d) + b x (c+d) = (a x c) + (a x d) + (b x c) + (b x d)

Final Result

Therefore, the expanded form of (a+b) x (c+d) is:

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

Example

Let's say a = 2, b = 3, c = 4, and d = 5. Substituting these values into the expanded form:

(2 x 4) + (2 x 5) + (3 x 4) + (3 x 5) = 8 + 10 + 12 + 15 = 45

We can also verify this by directly calculating (a+b) x (c+d):

(2 + 3) x (4 + 5) = 5 x 9 = 45

Conclusion

Expanding expressions like (a+b) x (c+d) is a fundamental skill in algebra. By understanding the distributive property and applying it systematically, we can simplify such expressions and obtain the correct results. This skill is crucial for solving a wide range of mathematical problems.

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