Simplifying Expressions Worksheets

What are like terms?

Terms are like terms when they have exactly the same variable part: $5x$ and $-2x$ are like terms, and so are 9 and $-3$, but $5x$ and $5y$ are not. Simplifying an expression means combining like terms by adding their coefficients, so that each kind of term appears only once.

The sign in front of a term belongs to that term. In $4x + 9 - x - 3$, the terms are $4x$, $9$, $-x$ and $-3$; the $-x$ has coefficient $-1$.

• Easy — three or four $x$-terms.
• Medium — $x$-terms and constants mixed together.
• Hard — $x$-terms, $y$-terms and sometimes a constant.

Worked examples

Easy: $5x - 2x + 7x$

All three are $x$-terms: $5 - 2 + 7 = 10$.

Medium: $4x + 9 - x - 3$

Group the $x$-terms and the constants: $4x - x = 3x$ and $9 - 3 = 6$.

Hard: $3x - 2y + 5 + x + 6y$

Combine $x$ with $x$ and $y$ with $y$; the 5 has no partner.

Check your answers

Substitute small numbers into the original and the answer. With $x = 2$ and $y = 1$ in the hard example: $6 - 2 + 5 + 2 + 6 = 17$ and $8 + 4 + 5 = 17$.

Common mistakes

• Combining unlike terms. $4x + 4y$ is already simplified; it is not $8xy$ or $8x$.
• Leaving the sign behind. In $4x + 9 - x - 3$, the term is $-x$, so the $x$-terms give $3x$, not $5x$.
• Forgetting the invisible 1. $x$ means $1x$, so $-7x - x = -8x$.
• Adding a constant to an $x$-term. $3x + 6$ cannot become $9x$.

Sample problems

These problems come from the same generator as the worksheet above, three at each difficulty level. Press Generate for a fresh set.

Easy

1. $-4x + 5x + x - 5x =$
2. $-4x - 2x - 7x =$
3. $x - 5x + 7x =$

Medium

4. $9 - 8 + 8x + 2 - 4x =$
5. $3 - 7x + 8 + 6x + 9x =$
6. $2 - 3x - 9x - 9 + 8x =$

Hard

7. $5x + 8y + 4x + 8x + 6y =$
8. $-4y + 4x + 2x + 3y + 5y + 3 + 7x =$
9. $3y + y + 9x + 2y - 5x =$

Tips for teachers and parents

• Colour or underline each kind of term (for example $x$-terms in one colour, constants in another) on the first few worksheets.
• Rewriting subtraction as adding a negative ($- x$ as $+ (-x)$) helps students who lose signs.
• This skill is used in every later topic: the distributive property and solving equations both end by combining like terms.

Related topics

• Distributive Property Algebra
• Solving Equations Algebra
• Polynomial Multiplication Algebra 2