Ready-to-teach

Clear steps, examples, and practice in one printable page.

Misconception-proof

Highlights common mistakes and how to fix them quickly.

Open license

CC0: free to copy, adapt, and share without attribution.

Quick overview

This free expressions worksheet for grades 7-8 builds confidence with combining like terms and distributing.

Lesson plan snapshot

15-20 min

Warm-up (3 min): combine like terms in a quick example.
Model (5 min): solve the worked example together.
Guided practice (5 min): complete problems 1-3 as a group.
Independent practice (7 min): finish the remaining problems.

Materials: color highlighters, pencil

Learning targets

Combine like terms to simplify expressions.
Use the distributive property accurately.
Evaluate expressions when given a value for the variable.

Step-by-step approach

1Group like terms (same variable and exponent).
2Add or subtract the coefficients of like terms.
3Use the distributive property to remove parentheses.
4Substitute values carefully and compute.

Common mistakes

Mistake

Combining unlike terms (x + x^2).

Try instead

Only combine terms with the same variable and exponent.

Mistake

Forgetting to multiply both terms inside parentheses.

Try instead

Multiply the factor by each term in the parentheses.

Mistake

Sign errors when distributing negatives.

Try instead

Treat a negative sign as multiplying by -1.

Worked example

Guided

Simplify:

3(x + 4) - 2x

Distribute: 3(x + 4) = 3x + 12.
Now combine like terms: 3x + 12 - 2x.
3x - 2x = x, so the result is x + 12.

Answer: x + 12

Related resources

Equations

Solve one- and two-step equations with clear steps.

View resource

Integers

Number line reasoning and integer operations.

View resource

Word problems

Translate scenarios into equations.

View resource

Practice problems

10 problems • 15 min

Printable worksheet

1
Simplify: $2x + 3x$
2
Simplify: $8x + 8x$
3
Evaluate $6x + 1$ for $x = 8$ .
4
Simplify: $2x + 4 + 5x + 2$
5
Evaluate $4x + 3y$ for $x = 4$ and $y = 2$ .
6
Simplify: $3x + 8x$
7
Simplify: $3x + 2x$
8
Evaluate $2x + 3y$ for $x = 2$ and $y = 4$ .
9
Simplify: $2x + 4 + 5x + 3$
10
Evaluate $3x + 4$ for $x = 6$ .

Answer key

10 answers

11) 5x
22) 16x
33) 49
44) 7x + 6
55) 22
66) 11x
77) 5x
88) 16
99) 7x + 7
1010) 22

Teacher tips

TUse color-coding to group like terms.
THave students say the distributive rule aloud before applying it.
TCheck simplification by plugging in a value.

Parent tips

PAsk your child to circle like terms before combining.
PWatch for sign changes when parentheses are removed.
PEncourage them to check answers with substitution.

Open license

You are free to copy, adapt, and share these materials. No attribution required. Released under Creative Commons CC0 1.0 (public domain).