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When simplifying algebraic expressions, it's crucial to understand the concept of like terms. Like terms are terms that have the identical variable parts raised to the same power. In other words, they share the same combination of variables and exponents. For example, in the expression \(5y^3 + 6y^3 - 3y^2 - 4y^2\), the terms \(5y^3\) and \(6y^3\) are like terms because they both contain \(y^3\). Similarly, \(-3y^2\) and \(-4y^2\) are like terms since they both have \(y^2\).
Identifying like terms is the first step in simplifying algebraic expressions. By grouping these similar terms, the process becomes much more manageable. This allows you to combine them effectively and simplify the overall expression.

After identifying like terms, the next step is to combine their coefficients. The coefficient is the numeric part of the term that is multiplied by the variable part. For instance, in the term \(5y^3\), the coefficient is 5.
To combine coefficients, simply add or subtract them, depending on their signs. Take the example \(5y^3 + 6y^3\). Here, the coefficients are 5 and 6. Adding them together gives you 11, resulting in \(11y^3\). Similarly, for the terms \(-3y^2 - 4y^2\), combine the coefficients -3 and -4. This operation is a subtraction of negative numbers, so you end up with -7, leading to \(-7y^2\).
Combining coefficients is straightforward but crucial for arriving at the simplified form of the expression.

A key aspect of handling algebraic expressions involves understanding the powers of variables. The power, or exponent, indicates how many times the variable is multiplied by itself. For instance, in \(y^3\), the exponent 3 means \(y \times y \times y\).
It's essential to remember that only terms with the same powers of variables can be combined. This is why \(5y^3\) and \(6y^3\) can be combined, but \(5y^3\) and \(-3y^2\) cannot.
Recognizing the powers of variables helps ensure that you are correctly grouping like terms and appropriately combining their coefficients. This understanding is fundamental to correctly simplifying any algebraic expression.