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The distributive law is a fundamental property in algebra. It allows us to multiply a single term by each term within parentheses. This is very useful when simplifying expressions. In the given problem, we're tasked with simplifying the expression: \[7a - (2a + 5)\].
To apply the distributive law, we distribute the negative sign across the terms inside the parentheses.
This means: \( - (2a + 5) \) becomes \( -2a - 5 \).
Our expression now looks like this: \[7a - 2a - 5\].
Notice how we effectively removed the parentheses by distributing the negative sign.
When first learning about the distributive law, it might be helpful to practice with simpler numerical examples before tackling more complex algebraic ones. Remember, mastering this property will greatly assist in simplifying expressions and solving equations.

Simplifying expressions involves making them as compact and manageable as possible. This often requires a combination of several algebraic techniques.
One common technique is to apply the distributive law, as we did in the previous section.
Another essential step in simplifying expressions is to combine like terms. Our modified expression after distribution was: \[7a - 2a - 5\].
Notice how we have two terms that both involve the variable \(a\).
To simplify, we need to combine these like terms: \(7a - 2a\) simplifies to \(5a\).
Now, our expression looks like this: \[5a - 5\].
Simplifying expressions helps in a variety of mathematical contexts, from solving equations to graphing functions. The goal is to make the expression as simple as possible while retaining its original value.

Like terms are terms that have the same variable raised to the same power. They can be combined through addition or subtraction.
Let's take another look at our expression: \[7a - 2a - 5\].
Here, \(7a\) and \(-2a\) are like terms because they both involve the variable \(a\) raised to the first power.
Combining these like terms involves adding or subtracting their coefficients (the numerical part): \( 7 - 2\) results in \( 5a\).
Thus, our expression simplifies to: \[5a - 5\].
Understanding how to identify and combine like terms is crucial for simplifying algebraic expressions.
It makes solving equations easier and helps in clearly expressing mathematical ideas.
Always remember, only terms with exactly the same variable components can be combined. This ensures that the expression remains accurate and meaningful.