8.2 Simplifying and collecting like terms — Learn

Prerequisites: basic algebraic notation and arithmetic with positive and negative numbers.

By the end of this section you can: simplify expressions by collecting like terms and constants.

Covers: A4.

Learn the method

Like terms have the same variable part. For example, $3x$ and $8x$ are like terms, but $3x$ and $3y$ are not.

To collect like terms, add or subtract their coefficients. The variable part stays unchanged.

Constants are like terms with no variable. Collect them separately from terms containing letters.

For $5x+2+3x-7$, collect the $x$ terms and the constants: $5x+3x+2-7=8x-5$.

Worked example. Simplify $6x+4-2x+3$.

$6x+4-2x+3$

$=(6-2)x+(4+3)$ — group the $x$ terms and constants.

$=4x+7$

Watch out. You cannot collect $3x$ and $3y$ because their variable parts differ. Keep unlike terms separate, then check by substituting values.

You should now be able to

• simplify expressions by collecting like terms and constants.