91Ó°ÊÓ

In algebra, we work with expressions that combine numbers and variables. An algebraic expression is a mathematical phrase that can include numbers, variables, and operation signs like plus (+) or minus (-). For example, the expression from the exercise is -8uv + 6u + 12uv. Here, u and v are the variables, and -8, 6, and 12 are the numbers called coefficients. Expressions like these are the building blocks for algebraic equations and inequalities.

Coefficients are the numerical parts of terms in an algebraic expression. They are the numbers that multiply the variables. In our example -8uv + 6u + 12uv, the coefficients are -8, 6, and 12. They tell us how many times to multiply the variables u and v. When combining like terms, we focus on the coefficients to simplify the expression. If we combine -8uv and 12uv, we add the coefficients -8 and 12. Calculating -8 + 12 gives us 4. So, -8uv + 12uv simplifies to 4uv.

To simplify an algebraic expression, we often need to combine like terms. Like terms are terms that have the same variables raised to the same power. For instance, in the expression -8uv + 6u + 12uv, the terms -8uv and 12uv are like terms because they both contain the variables u and v. The term 6u is not a like term with -8uv or 12uv because it only has the variable u.
Combining like terms helps to simplify expressions. First, identify the like terms. Then, add or subtract the coefficients. For our exercise, combining -8uv and 12uv to get 4uv, and leaving 6u as it is, results in the simplified expression 4uv + 6u. This process makes algebraic expressions easier to understand and work with.