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In algebra, combining like terms is a fundamental technique to simplify expressions. It's akin to organizing categories of similar items. Like terms have the same variable raised to the same power. This means that only the coefficients — the numbers in front of these variables — need to be combined. Let's consider the expression: - The expression \(-3y^2 - 4y + 2y^2 + y - 1\) contains both quadratic ( \(y^2\)) and linear ( \(y\)) terms.- To combine like terms, add or subtract the coefficients of terms with the same variable and the same exponent: - Combine the quadratic terms: \(-3y^2 + 2y^2 = -y^2\). - Combine the linear terms: \(-4y + y = -3y\). Remember, constants, like \(-1\), do not have variables, so they remain unchanged.

Simplifying expressions is all about making them easier to work with without changing their value. The goal is to rewrite the expression in a form that is most manageable and concise.When simplifying, you need to:- Remove any unnecessary parentheses when addition only is involved.- Combine all like terms, as discussed earlier. This reduces the number of terms, making it cleaner and often reducing room for calculation errors.- Ensure there are no further operations that can be simplified.For example, with the expression from the exercise:\(-3y^2 - 4y + 2y^2 + y - 1\), we simplified it to:\(-y^2 - 3y - 1\).Aside from making calculations easier, this step forms the groundwork for solving equations or performing substitutions efficiently.

Algebraic expressions are combinations of numbers, variables, and arithmetic operations — addition, subtraction, multiplication, and division. Gaining a strong understanding of algebraic expressions is crucial, as they form the basis of algebra. Here's what makes up an algebraic expression:- **Variables**: Usually letters like \(y\) or \(x\) that represent numbers whose exact values are not yet specified.- **Coefficients**: Numbers that multiply variables (e.g., \(-3\) is the coefficient in \(-3y^2\)).- **Constants**: Numbers on their own, without variables (e.g., \(-1\) in the given expression).- **Terms**: Each piece of the expression separated by plus or minus signs.To effectively work with algebraic expressions, one must become skilled in operations such as combining like terms and simplifying expressions, both of which serve as cornerstones for solving algebraic equations and understanding mathematical models.