Algebra - Simplifying Expressions and Collecting Like Terms

A Variable is a letter or symbol, such as $x$ or $y$, used to represent an unknown number. Think of it as a placeholder or an empty box where any value can be placed.

An Algebraic Term consists of a number (the coefficient) and a variable multiplied together, like $5x$. Visually, $5x$ can be imagined as five separate $x$ blocks grouped together: $x + x + x + x + x$.

Like Terms are terms that have the exact same variables raised to the exact same powers. For example, $3ab$ and $7ab$ are like terms because they share the variable part $ab$, while $3a$ and $3b$ are 'unlike' terms because their variables are different.

Collecting Like Terms is the process of simplifying an expression by adding or subtracting the coefficients of terms that are 'like'. Imagine grouping all the apples (term $a$) in one basket and all the bananas (term $b$) in another to find the total count for each.

The Sign Property states that the plus or minus sign directly in front of a term belongs to that term. When rearranging an expression like $4x - 5 + 2x$, it is helpful to visualize each term inside a box including its sign: $[+4x] [-5] [+2x]$.

Constants are numbers that do not have a variable attached to them, such as $7$ or $-12$. In an expression, all constants are considered like terms and should be combined together.

The Invisible One rule means that if a variable appears without a number in front, its coefficient is $1$. For example, $x$ is the same as $1x$, and $-y$ is the same as $-1y$.

Simplifying does not change the value of the expression; it just makes it shorter and easier to read. An expression like $x + x + x$ is more efficiently written as $3x$.