Streamlining Algebra: The Art of Collecting Terms

Imagine you have a basket full of assorted fruits. To know what you have at a glance, you'd group the same types of fruits together. In algebra, terms are like these fruits, and collecting like terms involves grouping together those that are similar, so the expression becomes easier to understand and work with. Let's learn how to do this seamlessly.

Understanding Like Terms

Before we start organizing, we need to know what "like terms" are. Like terms are terms that contain the same variables raised to the same power. The coefficients (numbers in front of the variables) can be different. For instance, $2x$ and $5x$ are like terms, but $2x$ and $2x^2$ are not, as the powers of $x$ differ.

Collecting Like Terms: Step-by-Step

1. Identify Like Terms: Look through the expression to find terms that have the same variable with the same exponent.
2. Add or Subtract Coefficients: Depending on the operation between them, add or subtract the coefficients of these like terms. Keep the variable part unchanged.
3. Repeat with all sets of like terms: Go through the expression until all like terms are collected.
4. Simplify: The expression is now simplified, with each variable represented just once.

Example of Collecting Terms

Simplify the expression: $4a + 3b - 2a + b$.

Collect like terms: $4a - 2a$ becomes $2a$, and $3b + b$ becomes $4b$.

The simplified expression is $2a + 4b$.