## Expanding (x + 10)^2: A Trinomial Exploration

The expression (x + 10)^2 represents the square of a binomial, which expands into a **trinomial**. Understanding how to expand this expression is crucial in algebra and has applications in various fields.

### Understanding the Concept

The expression (x + 10)^2 signifies multiplying the binomial (x + 10) by itself.

**Here's the expansion:**

(x + 10)^2 = (x + 10)(x + 10)

### Using the FOIL Method

To expand the expression, we can utilize the **FOIL method**, which stands for **First, Outer, Inner, Last**. This method helps systematically multiply each term in the first binomial by each term in the second binomial:

**First:** x * x = x^2

**Outer:** x * 10 = 10x

**Inner:** 10 * x = 10x

**Last:** 10 * 10 = 100

Adding all these products together, we obtain:

(x + 10)^2 = **x^2 + 10x + 10x + 100**

### Simplifying the Trinomial

Combining the like terms (10x and 10x), we get the simplified trinomial:

(x + 10)^2 = **x^2 + 20x + 100**

### The Trinomial's Structure

The expanded trinomial (x^2 + 20x + 100) follows a specific pattern:

**First term:**The square of the first term of the binomial (x^2)**Middle term:**Twice the product of the two terms in the binomial (2 * x * 10 = 20x)**Last term:**The square of the second term of the binomial (10^2 = 100)

### Generalization

This pattern holds true for any binomial squared:

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

### Conclusion

Understanding how to expand (x + 10)^2 into a trinomial using the FOIL method or recognizing the pattern is a fundamental skill in algebra. This knowledge allows for simplifying expressions, solving equations, and tackling more complex mathematical problems.