91Ó°ÊÓ

Simplifying algebraic expressions makes them easier to understand and work with. The primary goal is to combine similar terms so that the expression is as short and organized as possible.
To simplify the expression we were given: \( 9c - 8d + 2c - 5d + 3 \), we need to follow some simple steps. First, identify the terms that can be combined, a process known as combining like terms. Once these terms are grouped, we can then add or subtract their coefficients as needed to simplify the expression further. By doing this, we turn a long expression into a more manageable one.
For example, grouping like terms based on the variable or constants is key. Let's delve deeper into these important concepts for better understanding.

Like terms are terms that have the same variable raised to the same power. For instance, in the expression \( 9c - 8d + 2c - 5d + 3 \), the terms \( 9c \) and \( 2c \) are like terms because they both contain the variable 'c'. Similarly, \( -8d \) and \( -5d \) are also like terms because they both contain 'd'.
Identifying Like Terms:
- Look for terms with the same variable part.
- Ignore the coefficients at first and focus on the variable.
Examples of Like Terms:
- \( 3x \) and \( 2x \)
- \( 4y^2 \) and \( -y^2 \)
Non-Examples:
- \( 5x \) and \( 5y \)
- \( 3x \) and \( 3x^2 \)
Identifying and combining like terms helps simplify expressions efficiently. This simplification makes solving algebraic equations easier and clearer.

Coefficients are the numerical part of a term that is multiplied by the variable. In the term \(9c\), 9 is the coefficient of the variable 'c'. When combining like terms, you add or subtract their coefficients while keeping the variable part unchanged.
How to Combine Coefficients:
- Identify like terms in the expression (same variable and power).
- Add or subtract their coefficients.
Example:
Given the expression \( 9c + 2c \), combine the coefficients 9 and 2 to get 11. So, \( 9c + 2c = 11c \).
Similarly, for the terms involving 'd' from our exercise, combining \( -8d \) and \( -5d \) results in \( -13d \). After combining all like terms, including any constants, the simplified expression from the exercise becomes: \( 11c - 13d + 3 \).
Understanding coefficients helps in efficiently solving and simplifying algebraic expressions.