What makes terms alike
A term is a single piece of an expression, separated from its neighbours by a plus or minus sign. In \(5x + 3y - 2\) the terms are \(5x\), \(3y\) and \(-2\).
Two terms are like terms when they have exactly the same letters raised to exactly the same powers. Only the number in front, the coefficient, is allowed to differ.
- Like terms
- Terms with the identical letter part, for example \(4x\) and \(7x\), or \(2ab\) and \(9ab\). They can be added or subtracted into a single term.
So \(4x\) and \(7x\) are alike, but \(4x\) and \(4y\) are not, and neither are \(4x\) and \(4x^2\). The power matters: \(x\) and \(x^2\) are different kinds of thing.
Combining like terms
To combine like terms, add or subtract their coefficients and keep the letter part unchanged. Think of \(4x\) as "four \(x\)s". Four of them plus three of them is seven of them, so \(4x + 3x = 7x\). You never change the \(x\) itself.
Simplify \(8a + 5 - 3a + 6\).
The sign travels with the term
When you shuffle terms around, carry the sign in front of each one with it. In \(8a - 3a\) the \(3a\) is negative, so it stays a subtraction wherever it lands.
More than one variable
Many expressions mix several letters. The rule does not change: keep each family of like terms separate and combine within each family. Terms with different letters simply stay apart in the answer.
Simplify \(7x + 4y - 3x + 2y\).
The same care applies to products of letters: \(2ab\) and \(5ab\) are alike and give \(7ab\), but \(2ab\) and \(5a\) are not alike, so they cannot be joined.
Common slips
Most marks lost here come from a handful of repeatable errors. Communicating your working clearly, which is Criterion C, makes them easy to catch.
| Slip | Fix |
|---|---|
| Merging \(x\) with \(x^2\) | Different powers are unlike; keep them apart. |
| Dropping a minus sign | Move each sign with its term. |
| Combining \(3x\) and \(3y\) into \(6xy\) | Different letters stay separate; leave as \(3x + 3y\). |
Check yourself
1. Simplify \(8a + 3 - 5a + 6\). +
The \(a\) terms give \(8a - 5a = 3a\). The numbers give \(3 + 6 = 9\). Answer: \(3a + 9\).
2. Simplify \(4x + 7y - x - 2y\). +
The \(x\) terms: \(4x - x = 3x\). The \(y\) terms: \(7y - 2y = 5y\). Answer: \(3x + 5y\).
3. Simplify \(3p + 2q - 5p + q\). +
The \(p\) terms: \(3p - 5p = -2p\). The \(q\) terms: \(2q + q = 3q\). Answer: \(-2p + 3q\).
Part of the Standard Maths library. Spotted an error or want a topic added? That feedback makes the notes better.