## Understanding (k + 5)^2

(k + 5)^2 is a mathematical expression representing the square of the binomial (k + 5). This means multiplying the binomial by itself:

**(k + 5)^2 = (k + 5)(k + 5)**

To simplify this expression, we can use the **FOIL method** (First, Outer, Inner, Last). This method helps us multiply two binomials systematically.

**Here's how it works:**

**First:**Multiply the first terms of each binomial:**k * k = k^2****Outer:**Multiply the outer terms of the binomials:**k * 5 = 5k****Inner:**Multiply the inner terms of the binomials:**5 * k = 5k****Last:**Multiply the last terms of each binomial:**5 * 5 = 25**

Now, combine the results:

**(k + 5)^2 = k^2 + 5k + 5k + 25**

Finally, simplify by combining like terms:

**(k + 5)^2 = k^2 + 10k + 25**

**Therefore, the expanded form of (k + 5)^2 is k^2 + 10k + 25.**

**Key Points:**

**The FOIL method**is a useful tool for multiplying binomials.- Expanding a binomial square results in a trinomial (an expression with three terms).
- The coefficient of the middle term (10k) is always twice the product of the terms in the original binomial (k and 5).
- The constant term (25) is always the square of the second term in the original binomial (5).

Understanding how to expand expressions like (k + 5)^2 is essential in algebra and other areas of mathematics. It allows you to simplify expressions and solve equations more effectively.