Algebra basics: collecting like terms and substituting

Algebra looks like a new language, but it's the same arithmetic you already know with one change: a letter holds the place of a number we don't know yet. Get comfortable with two skills here — collecting like terms and substituting — and the rest of school algebra has somewhere solid to stand.

What the letter means

In $3x$, the $x$ is just a number we haven't been told, and $3x$ means "three lots of $x$." So $x + x + x = 3x$. The number stuck to the front is the coefficient; the letter is the variable. That's the whole vocabulary you need to start.

Collecting like terms

You can only add or subtract terms that have the exact same letter part. Those are like terms. Think of it as adding things of the same kind:

But $3x + 5y$ stays as it is — apples and oranges don't combine. And watch the powers: $x$ and $x^2$ are not like terms either.

Collect the $x$ terms together, collect the plain numbers together, and leave the unlike ones apart.

Substituting numbers back in

To evaluate an expression, replace each letter with its value and work it out — minding the order of operations.

Find $2a + b^2$ when $a = 5$ and $b = 3$:

The one to watch: $2a$ means $2 \times a$, so put the multiplication in. Writing the numbers next to each other isn't enough once they're actual digits.

A coefficient of 1 is invisible, but it's there. $x$ means $1x$, so $x + 5x = 6x$, not $5x$. Forgetting that hidden $1$ is the most common slip when collecting terms.

Last revised 26 November 2024.