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Subtracting expressions, especially algebraic ones, can seem tricky at first. However, it's just like subtraction with numbers, but with variables involved. Let's break it down. In subtraction, you take one value away from another. In algebra, this means you disengage similar terms from each other. Consider \[(4 + 5a) - (-a - 5)\]. Here, you have two expressions:

• \(4 + 5a\)
• \(-a - 5\)

The subtraction means we want to take the entire second expression away from the first.
Keep in mind that subtracting an expression is not just about changing a single number. It's an operation that changes the entire value of the expression, possibly altering each term based on its sign.
That’s where the next concept, distributing negative signs, becomes crucial.

When you subtract expressions, distributing the negative sign is a crucial step. This means you apply the negative sign to each term of the expression that follows it. For example: \[(4 + 5a) - (-a - 5)\].
By distributing the negative sign across the terms inside the brackets, each negative sign becomes positive. Thus:

• Change \(-a\) to \(+a\)
• Change \(-5\) to \(+5\)

As a result, the expression becomes \(4 + 5a + a + 5\).
This step is essential because each operation in algebraic expressions can change based on the presence of negative or positive signs. Releasing the parentheses correctly translates a subtraction operation into an equivalent addition, enabling simplification.

Once you've distributed any negative signs, your next task is to combine like terms. "Like terms" are terms that have the same variable raised to the same power.
In our expression, \(4 + 5a + a + 5\), the like terms must be identified and added together:

• Add the constant numbers: \(4\) and \(5\), which results in \(9\).
• Add the terms with the variable \(a\): \(5a\) and \(a\), summing up to \(6a\).

By combining these terms correctly, we simplify the expression to \(9 + 6a\).
This process is vital as it helps compress expressions into simpler forms, making them easier to work with in further calculations or solutions.