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In algebra, like terms are terms that contain the same variables raised to the same power. For example, in the expression \(12x - 11 + 5x + 3\), both \(12x\) and \(5x\) are like terms because they share the same variable, \(x\), raised to the first power. Similarly, the numbers \(-11\) and \(3\) are both constants, or terms without variables, and are therefore like terms with each other.

Recognizing like terms is crucial because only like terms can be combined through addition or subtraction. This step reduces the complexity of expressions, making them easier to work with. Look for terms that share the same variable and exponent; those are the terms you can "combine."

This foundation helps streamline algebraic processes and provides clarity when manipulating polynomials and other algebraic expressions.

Once you've identified like terms, the next step in simplifying expressions is to combine them. Combining like terms involves adding or subtracting their coefficients while keeping the variable part unchanged. For instance, in the operation \(12x + 5x\), since both terms share the same variable \(x\), you add the coefficients, resulting in \(17x\).

Here are some simple tips for combining like terms:

• Line up the like terms vertically to avoid confusion.
• Add or subtract the coefficients of like terms carefully.
• Always keep the variable and its power part the same.

Combining like terms simplifies expressions and is a foundational skill in algebra that prepares you for more complex operations.

Polynomial addition involves summing up polynomials by combining like terms. A polynomial is a mathematical expression consisting of variables, coefficients, and constants, structured in terms potentially involving powers and operations of addition and subtraction. Consider the example \(12x - 11 + 5x + 3\).

Here’s a simple guide to add polynomials:

• First, identify all like terms in each polynomial.
• Align the polynomials vertically to intuitively match like terms
• Combine the like terms by adding or subtracting their coefficients as was demonstrated to achieve \(17x - 8\).

Adding polynomials is a critical skill in algebra that relies on understanding and manipulation of like terms, helping you to simplify or solve equations seamlessly.