## Expanding the Expression (x+5)(x+5)

This expression is a perfect square trinomial, meaning it represents the product of the same binomial multiplied by itself. Let's explore how to expand it:

### Using the FOIL Method

**FOIL** stands for **F**irst, **O**uter, **I**nner, **L**ast. This method helps us systematically multiply each term of the first binomial with each term of the second binomial:

**First:**Multiply the first terms of each binomial: x * x =**x²****Outer:**Multiply the outer terms of the binomials: x * 5 =**5x****Inner:**Multiply the inner terms of the binomials: 5 * x =**5x****Last:**Multiply the last terms of each binomial: 5 * 5 =**25**

Now, we add all the results together:

x² + 5x + 5x + 25

Finally, combine the like terms:

**x² + 10x + 25**

Therefore, the expanded form of (x+5)(x+5) is **x² + 10x + 25**.

### Using the Square of a Binomial Formula

We can also use the formula for the square of a binomial:

(a + b)² = a² + 2ab + b²

In this case, a = x and b = 5. Substituting these values into the formula, we get:

(x + 5)² = x² + 2(x)(5) + 5²

Simplifying, we obtain the same result as before:

**x² + 10x + 25**

Both methods lead to the same answer, so you can choose whichever one you find easier to understand and apply.