To expand and simplify the expression (x+5)(x+8), we can use the distributive property of multiplication over addition. This property states that when we have a multiplication of two terms being added together, we can distribute the multiplication to each term individually.
Here's how we can do it step by step:
1. Start with the expression (x+5)(x+8).
2. Apply the distributive property by multiplying each term in the first set of parentheses by each term in the second set of parentheses:
(x * x) + (x * 8) + (5 * x) + (5 * 8)
Simplifying each multiplication, we get:
x^2 + 8x + 5x + 40
3. Combine like terms. The terms 8x and 5x can be added together:
x^2 + 13x + 40
Therefore, the expanded and simplified form of (x+5)(x+8) is x^2 + 13x + 40.
To better understand this, let's consider an example. Suppose x = 2.
If we substitute x = 2 into the original expression, we have (2+5)(2+8).
Following the steps above, we get:
(2^2) + (13 * 2) + 40
= 4 + 26 + 40
= 70
So when x = 2, the expression (x+5)(x+8) equals 70.
Remember, when expanding and simplifying expressions, it's important to apply the distributive property correctly and combine like terms to get the final result.