## Expanding and Simplifying (x + y)^2

The expression (x + y)^2 is a common algebraic expression that appears in various mathematical contexts. It represents the square of the sum of two variables, **x** and **y**. Expanding and simplifying this expression is a fundamental skill in algebra.

### Understanding the Concept

(x + y)^2 essentially means multiplying the binomial (x + y) by itself:

(x + y)^2 = (x + y)(x + y)

To expand this expression, we can use the **distributive property**:

**Multiply the first term of the first binomial by each term of the second binomial:**- x * x = x^2
- x * y = xy

**Multiply the second term of the first binomial by each term of the second binomial:**- y * x = xy
- y * y = y^2

Combining the results, we get:

(x + y)^2 = x^2 + xy + xy + y^2

### Simplifying the Expression

Notice that we have two identical terms, **xy**, in the expanded form. Combining these terms, we get the simplified expression:

(x + y)^2 = **x^2 + 2xy + y^2**

### Key Points to Remember

- The expanded form of (x + y)^2 is
**x^2 + 2xy + y^2**. - This expression represents the
**square of the first term**(x^2),**twice the product of the two terms**(2xy), and the**square of the second term**(y^2). - This formula can be used to expand and simplify various algebraic expressions involving squared binomials.

### Example

Let's say we want to expand and simplify the expression (2a + 3b)^2. Applying the formula:

(2a + 3b)^2 = (2a)^2 + 2(2a)(3b) + (3b)^2

Simplifying further:

(2a + 3b)^2 = **4a^2 + 12ab + 9b^2**

By understanding and applying the formula for expanding (x + y)^2, we can effectively manipulate and simplify algebraic expressions, paving the way for solving more complex equations and tackling higher-level mathematics.