91Ó°ÊÓ

When simplifying an algebraic expression, one crucial step is combining like terms. Like terms are terms that have the same variables raised to the same powers. For instance, in the expression \(-9.6r + 2.7 - 8.5r - 2.7\), we have two sets of like terms: \(-9.6r\) and \(-8.5r\) (both contain the variable \(r\)) as well as 2.7 and -2.7 (both are constant terms without variables).
To simplify, we group and add these like terms. This process helps in reducing the expression to its simplest form. Grouping like terms together makes the calculation more straightforward and keeps the equation tidy. For example, with variable terms, we add their coefficients, and for constant terms, we sum them directly.

Variable terms in an expression include numbers (coefficients) multiplied by variables. For instance, in \(-9.6r + 2.7 - 8.5r - 2.7\), -9.6r and -8.5r are variable terms. Here, the 'r' is the variable, and -9.6 and -8.5 are the coefficients.
When simplifying, combine these by adding the coefficients: \(-9.6 - 8.5\). This gives us \(-18.1\), so the combined variable term becomes \(-18.1r\).
Remember, only like variable terms can be combined. This means they must have exactly the same variable part. By focusing on the coefficients, the expression stays clean and accurately simplified.

Constant terms are terms in an expression without any variables. They stand alone as fixed numbers. In the given exercise, 2.7 and -2.7 are the constant terms. Sometimes, constants directly impact the expression's value, and sometimes their sum could be zero, thereby simplifying the expression further.
In our example, we add the constant terms: 2.7 - 2.7, which equals 0. Including 0 in the final expression does not alter its value, hence it can be omitted if it simplifies the final result.
Understanding how to handle constant terms and their combinations can significantly simplify your calculations and make the expressions easier to manage.