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§ Expressions & Algebra·Grades 6–7

Simplify Expressions Worksheets

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Easy

10 problems

Medium

20 problems

Hard

20 problems

Mixed

30 problems

Free printable simplify expressions worksheets with step-by-step answer keys. Every worksheet is uniquely generated so students never see the same problems twice. Topics covered range from combine like terms (one variable) at the easy level through to expand two brackets and simplify at the advanced level.

CCSS.6.EECCSS.7.EE

What is simplify expressions?

Simplifying expressions means combining like terms and reducing mathematical expressions to their most compact form. The process involves identifying terms with identical variables and powers, then adding or subtracting their coefficients. For example, 5x + 3x simplifies to 8x by combining the coefficients 5 and 3.

Why it matters

Expression simplification forms the foundation for solving equations in algebra, calculus, and higher mathematics. Engineers use simplified expressions to optimize designs — a structural engineer might reduce 4L + 6L + 2L to 12L when calculating total beam length. In computer programming, simplified expressions run faster and use less memory. Financial analysts simplify complex interest formulas to make calculations more efficient. The skill appears throughout CCSS standards, from Grade 6 expressions (CCSS.6.EE) through Algebra I structure interpretation. Students who master simplification can solve quadratic equations, work with polynomials, and manipulate trigonometric expressions. The process also develops pattern recognition skills essential for mathematical reasoning and problem-solving across all STEM fields.

Common mistakes to watch for

  • ✗Adding coefficients of unlike terms, such as writing 3x + 2y = 5xy instead of leaving it as 3x + 2y.
  • ✗Forgetting that terms without visible coefficients have coefficient 1, leading to x + 3x = 3x instead of 4x.
  • ✗Incorrectly combining terms with different powers, like writing 2x + 3x² = 5x³ instead of keeping them separate as 2x + 3x².
  • ✗Making sign errors when distributing negative signs, such as expanding -(3x + 4) as -3x + 4 instead of -3x - 4.

Questions teachers ask

What are like terms in algebra?+
Like terms are terms that contain exactly the same variables raised to the same powers. For example, 3x and 7x are like terms because both contain the variable x to the first power. However, 2x and 3x² are unlike terms because the powers of x are different.
How do you combine like terms?+
To combine like terms, add or subtract their coefficients while keeping the variable part unchanged. For instance, 4a + 6a = 10a because 4 + 6 = 10. The variable 'a' remains the same throughout the process.
Can you simplify expressions with different variables?+
Different variables cannot be combined into a single term. An expression like 5x + 3y cannot be simplified further because x and y are different variables. The simplified form remains 5x + 3y.
What does it mean to expand brackets?+
Expanding brackets means multiplying the term outside the brackets by each term inside. For example, 6(x + 3) expands to 6x + 18 by multiplying 6 by x and 6 by 3 separately.
How do you check if an expression is fully simplified?+
An expression is fully simplified when no like terms remain that can be combined and all brackets have been expanded. Check that terms with identical variable parts have been added together and no further operations are possible.
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Pick a difficulty

Click any level to open the generator with that difficulty pre-selected.

Beginner

Generate →
Concepts
Combine like terms (one variable)
Range
coefficients 1–9
Steps
2 steps
Example
3x + 5x

Easy

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Concepts
Combine like terms (two variables)
Range
coefficients 1–8, add/subtract
Steps
2 steps
Example
2a + 3b + 5a − b

Medium

Generate →
Concepts
Expand single bracket
Range
multiplier 2–9, coefficients 1–6
Steps
3 steps
Example
4(3x + 5)

Hard

Generate →
Concepts
Expand two brackets and simplify
Range
multipliers 2–5, constants −6 to 6
Steps
3 steps
Example
3(2x + 4) + 2(x − 3)

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