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To simplify algebraic expressions, one of the essential steps is combining like terms. Like terms are terms that have the same variable raised to the same power. For example, in the expression \(12b + b\), both terms contain the variable \(b\).

When you combine like terms, you add or subtract their coefficients. Here, the coefficients of \(12b\) and \(b\) are 12 and 1, respectively. So, you simply add these coefficients together: \(12 + 1 = 13\).
Thus, the expression \(12b + b\) simplifies to \(13b\).

This process makes algebraic expressions much simpler and easier to handle in subsequent calculations.

The coefficient in an algebraic expression is the numerical factor that multiplies the variable. For instance, in the expression \(12b + b\), the coefficients are 12 and 1 (since \(b\) is the same as \(1b\)).

Understanding coefficients is crucial because they tell you how many units of a variable you have. When you combine like terms, you are essentially combining the coefficients. So, in \(12b + b\), adding the coefficients 12 and 1 gives you 13.

This makes the simplified form of the expression \(13b\). Identifying and working with coefficients accurately is key to mastering algebra.

Variables are symbols that represent numbers and are usually denoted by letters such as \(b, x, y,\) etc. In the given expression \(12b + b\), \(b\) is the variable.

Variables allow us to write general formulas and solve problems that involve unknown quantities. When simplifying expressions, it's important to handle variables and their coefficients correctly.

In our example, after identifying like terms (terms with the same variable), we only needed to add their coefficients. The variable \(b\) remains as it is, but with a new coefficient formed by combining the old coefficients.

Thus, \(12b + b\) simplifies to \(13b\). It's like saying you have 12 apples (12b) and you get 1 more apple (b), resulting in 13 apples (13b).