Long expressions can usually be made shorter. Learn to group matching pieces together, and to "spread" a multiplier across a set of parentheses.
A term is a single piece of an expression. Terms are separated by + and − signs. In 3x + 2x + 5, there are three terms: 3x, 2x, and 5.
The number in front is the coefficient, and the letter is the variable. A term with no variable, like 5, is called a constant.
Like terms have the exact same variable part. You can only add or subtract terms that are alike — just like you can't add apples to oranges.
Both have x — they combine.
Different variables — they stay separate.
To combine like terms, add the coefficients and keep the variable the same. Think of x as a box: 3 boxes plus 2 boxes is 5 boxes.
Plain numbers (constants) combine with each other: 5 + 3 = 8. But a number and a variable term — like 5 and 3x — are not alike, so 5 + 3x just stays as 5 + 3x.
Here's a jumbled expression as tiles. Tap two like tiles to combine them — matching colors are like terms. Keep going until nothing else can be combined.
What about 2(x + 3)? The 2 is multiplying the whole group in parentheses. The distributive property says you multiply the 2 by each term inside — the 2 "spreads" to both pieces.
2(x + 3) means two copies of (x + 3): that's (x + 3) + (x + 3), which is x + x + 3 + 3 = 2x + 6. Distributing is just a shortcut for that.
Simplify each expression and type the result — for example, 5x + 6. Use a plus sign between terms and put the coefficient in front (like 3x). You earn a point for each one you get on the first try.