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When dealing with algebraic expressions, the distributive property is a tool you'll use frequently to simplify expressions. It allows you to eliminate parentheses by distributing a multiplier to each term within the parentheses. Here's how it works: if you have an expression like \(a(b + c)\), the distributive property enables you to expand this to \(ab + ac\).

In the exercise \(10-(11x-3)\), the distributive property comes into play when the negative sign, which is technically \( -1 \), distributes over the terms within the parentheses. This effectively changes the signs of the terms inside. Remembering that \( -1 \times b = -b \) and \( -1 \times -c = c \) will help you understand how \(10 - (11x - 3)\) simplifies to \(10 - 11x + 3\).

The key is to ensure every term inside the parentheses is multiplied by the number (or variable) outside the parentheses. This process makes dealing with complex expressions much more manageable.

Once you've used the distributive property, your expression might look a bit more spread out. That's where the concept of combining like terms comes in handy. Like terms are terms in an expression that have the exact same variable raised to the exact same power. The coefficients, or numbers in front of the variables, don't have to match--that's actually what you'll be combining.

In our exercise, after applying the distributive property, we're left with the expression \(10 - 11x + 3\). Here, the like terms are the constants, 10 and 3. They can be added together: \(10 + 3 = 13\). Therefore, our final expression becomes \(13 - 11x\). Remember that coefficients of like terms combine according to their arithmetic operations, and be mindful to respect the signs of each term when adding or subtracting them.

An algebraic expression, in essence, is a mathematical phrase that can contain ordinary numbers, variables (like \(x\) or \(y\)), and operators (like add, subtract, multiply, and divide). They don't have an equals sign as equations do; rather, they are expressions waiting to be simplified or manipulated in some way.

Our starting exercise, \(10-(11x-3)\), is a typical example. It contains constants (10 and 3), a variable (\(x\)), and operations (subtraction inside and outside of the parentheses). Simplifying algebraic expressions involves reducing them to the simplest form possible, which involves applying the distributive property and combining like terms as we've done here. The goal is to make the expression as straightforward as possible, often in preparation for solving equations or evaluating the expression for particular variable values.