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:

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)

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.