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Algebraic expressions are a combination of numbers, variables, and mathematical operations (such as addition, subtraction, multiplication, and division). These expressions can look complex at first, but understanding them is easier than you might think. In an algebraic expression, variables are symbols or letters that represent unknown values. Numbers are known values, while operations indicate the mathematical process involved.
Let's break down an example: if you have the expression \(5(3y - 2) - (7y + 2)\), it contains variables \(y\) alongside constants and operations like multiplication and subtraction. To tackle such expressions, you'll often use the distributive property and combine like terms, which are keys to simplifying them effectively.

Simplifying expressions means making them neater and easier to understand, usually by reducing them to fewer terms. You often use the distributive property to simplify expressions. The distributive property allows you to break down expressions by distributing a term across a sum or difference inside parentheses. For instance:
- In \(5(3y - 2)\), you can distribute \(5\) to both \(3y\) and \(-2\) to get \(15y - 10\).
- Similarly, for \(-(7y + 2)\), you distribute the implicit \(-1\) to both \(7y\) and \(2\), resulting in \(-7y - 2\).
After applying the distributive property and performing the multiplications, you'll need to combine any like terms to further simplify the expression.

Like terms are terms in an algebraic expression that have the same variable raised to the same power. In other words, they look alike except for the coefficients (the numerical part). Only like terms can be added or subtracted from each other. For example, in the expression obtained from the previous simplification step \(15y - 10 - 7y - 2\):
- \(15y\) and \(-7y\) are like terms because they both contain the variable \(y\) raised to the power of 1. You can combine them to get \(8y\).
- The constants \(-10\) and \(-2\) are also like terms since they don't contain any variables, and you can add them to get \(-12\).
Combining like terms helps in reaching the final simplified form of the expression, making the mathematical expression clearer and more concise.