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Like terms in algebra are terms that have the same variables raised to the same power. They can be added or subtracted just like regular numbers. For example, in the expression\(3x + 5x\), both terms are like terms because they share the same variable, \(x\). Thus, they can be combined to make \(8x\).
In contrast, consider the expression given in the original exercise, \(5ab + 11bc\). Here, \(ab\) and \(bc\) are not like terms. The reason is that they have different combinations of variables: one involves \(ab\) and the other involves \(bc\). To simplify expressions, only like terms can be combined.
If the variables or their exponents are different, the terms are not like terms, and hence remain separate in the expression. Identifying and understanding like terms are crucial for simplifying algebraic expressions.

Variables are symbols that represent numbers or values that can change. In algebra, they are typically represented by letters such as \(x, y,\) or \(z\). These letters allow us to write expressions that can be used for a variety of situations and numbers. For example, in the expression\(5ab + 11bc\), \(a, b,\) and \(c\) are the variables.
Variables are the heart of algebra and allow for the generalization of mathematical statements. Here are some basics about variables in algebra:

• They stand in for unknown values.
• They often represent relationships between numbers.
• Can be manipulated using mathematical operations.

In our exercise, each term has its own combination of variables \(ab\) and \(bc\). These different variables indicate the terms are unique from one another, leading to the conclusion that no further simplification through combining terms is possible.

Simplifying algebraic expressions is an essential skill in algebra. It involves reducing expressions to their simplest form. This can make them easier to understand and work with.
Here are some key simplification rules:

• Combine like terms: Only terms with the same variable and exponent can be added together.
• Use the distributive property when necessary: Bill ions are multiplied across terms inside parentheses.
• Simplify fractions and factor when possible to reduce expressions to a simpler form.

In our original exercise, simplifying \(5ab + 11bc\) means recognizing that \(ab\) and \(bc\) are not like terms. Since there are no like terms to combine, the expression is already in its simplest form.
This process highlights the importance of recognizing like terms and being clear about the role of each variable to accurately simplify expressions.