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Expanding (x + y)²: A Simple Guide
The expression (x + y)² is a fundamental concept in algebra and is frequently encountered in various mathematical applications. Understanding how to expand this expression is crucial for simplifying equations, solving problems, and building a strong foundation in algebra.
Understanding the Concept
Expanding (x + y)² essentially means multiplying the entire expression by itself:
(x + y)² = (x + y)(x + y)
The FOIL Method
One common method to expand this expression is the FOIL method:
First: Multiply the first terms of each binomial: x * x = x²
Outer: Multiply the outer terms of the binomials: x * y = xy
Inner: Multiply the inner terms of the binomials: y * x = xy
Last: Multiply the last terms of each binomial: y * y = y²
The Result
By combining the terms, we get the expanded form of (x + y)²:
(x + y)² = x² + xy + xy + y² = x² + 2xy + y²
Conclusion
Expanding (x + y)² yields the expression x² + 2xy + y². This simple yet essential concept serves as a foundation for various mathematical operations and applications. By understanding the FOIL method and the basic principles of multiplication, you can easily expand this and similar expressions in algebra.