91Ó°ÊÓ

Understanding how to simplify algebraic expressions is crucial for solving equations effectively. Simplification makes an equation or expression easier to work with and understand. Consider an expression like \(9a - 4a + 2a\). The process begins by identifying like terms, which are terms that share the same variable and exponent. In this instance, all terms have the variable 'a'.

To simplify, you combine these like terms. This means adding or subtracting the numerical coefficients while the variable part remains unchanged. Simplifying \(9a - 4a + 2a\) thus involves combining the coefficients (9, -4, and 2) corresponding to the variable 'a'. The simplified version of the expression, as shown in the exercise solution, is \(7a\).

When dealing with algebraic expressions, addition and subtraction are the fundamental operations used to combine like terms. Remember that only like terms can be combined; these are terms that have the same variables and exponents. For instance, \(a\) terms only combine with other \(a\) terms.

In the provided exercise, we add and subtract the coefficients of like terms. Adding \(9a + 2a\) and subtracting \(4a\), we follow the standard rules of arithmetic while treating the variable part as a common factor. It's similar to saying 'I have 9 apples, gain 2 more but lose 4.' Ultimately, you are left with 7 apples, or in the case of the algebraic expression, \(7a\).

Coefficients are the numbers found in front of variables in algebraic expressions and play a key role in the process of combining like terms. They dictate the 'quantity' of the variable they're attached to. For example, in the expression \(9a - 4a + 2a\), the coefficients are 9, -4, and 2. When simplifying the expression, pay attention to these coefficients.

The operation required to simplify is influenced by whether the coefficients are added or subtracted from one another, as dictated by the signs in front of them. In the exercise, to find the simplified expression, we calculate the sum of the coefficients as \(9 + (-4) + 2\), which equals 7. Hence, our simplified expression is \(7a\), indicating we have seven times the quantity 'a'.