Expand using the distributive property: 2(-3/2x - 9)
Show algebraic work: __________________________________
CCSS 7.EE.A.1 · distributive property both directions
Expanding and Factoring Linear Expressions Worksheets
Use the distributive property in both directions instead of treating expansion and factoring as unrelated tricks. Expansion items can include rational coefficients; factoring items use a clear greatest integer factor so the expected form is unambiguous.
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Expand & Factor Linear Expressions
Expand & factor expressions · Grade 7 standard · Seed 271801
1.
2.
Expand using the distributive property: 3(4x - 4)
Show algebraic work: __________________________________
3.
Factor the greatest integer factor: -30x - 18
Show algebraic work: __________________________________
4.
Expand using the distributive property: -3/2(6x + 5)
Show algebraic work: __________________________________
5.
Expand using the distributive property: 6(4x + 6)
Show algebraic work: __________________________________
6.
Factor the greatest integer factor: -5x + 10
Show algebraic work: __________________________________
7.
Factor the greatest integer factor: 6x - 42
Show algebraic work: __________________________________
8.
Factor the greatest integer factor: -20x - 28
Show algebraic work: __________________________________
9.
Expand using the distributive property: 5/2(-1/2x + 11)
Show algebraic work: __________________________________
10.
Expand using the distributive property: 1/2(5/2x + 1)
Show algebraic work: __________________________________
Construction rule: equations are built around known exact solutions, expression rewrites use exact rational arithmetic, 7.EE.3 money stays in integer cents, and inequality answer graphs are withheld until answers are revealed.
Expanding and factoring a linear expression
Expanding multiplies the outside factor by every term inside the parentheses. Factoring reverses that step: find the greatest common factor of the terms, write it outside, and put what is left inside parentheses. Check any factored answer by expanding it back to the original expression.
Worked examples
- Expand 3(2x − 5): multiply both terms, 3 × 2x = 6x and 3 × (−5) = −15, so the result is 6x − 15.
- Factor 12x + 18: the greatest common factor is 6, so 12x + 18 = 6(2x + 3).
- Factor 20x − 15: the common factor is 5, so 20x − 15 = 5(4x − 3). The subtraction sign stays inside the parentheses.
Common slips
- Multiplying only the first term. 3(2x − 5) is not 6x − 5.
- Changing the sign when factoring. 20x − 15 is 5(4x − 3), not 5(4x + 3).
- Not using the greatest common factor. 12x + 18 = 3(4x + 6) is correct but not fully factored, because 4x + 6 still has a common factor of 2.
How to use this worksheet
Have students expand every factored answer as a check. The answer key shows the factored form with the greatest common factor, so students can see if they stopped early.
Common Core connection
- 7.EE.A.1 · Apply properties of operations to add, subtract, factor, and expand linear expressions.
A practical match for the skill this worksheet practises, not a claim that one worksheet teaches or assesses the whole standard. Check the official math standards.
Note 1
Expansion multiplies the outside factor by every term inside the grouping symbols.
Note 2
Expanding 3(2x - 5) gives 6x - 15; stopping at 6x - 5 because the second term was not multiplied is the most frequent error.
Note 3
Factoring reverses distribution by identifying a common factor shared by both terms: 12x + 18 has GCF 6, so it factors to 6(2x + 3).
Note 4
Always verify a factored answer by distributing it back to the original expression.
Note 5
A subtraction inside the parentheses keeps its sign when you factor: 20x - 15 factors to 5(4x - 3), not 5(4x + 3).
Continue the 7.EE progression
Move to another Grade 7 algebra skill
Quick answers
Why use greatest integer factor on factoring items?
It gives a single classroom-friendly target form and avoids ambiguous fractional-factor answers.
Can expansion include fractions?
Yes. Standard and challenge modes can use exact rational coefficients.
How is 'expand' different from 'factor'?
They are inverse moves. Expanding removes parentheses by distributing; factoring adds parentheses by pulling out a common factor. 7.EE.A.1 expects fluency in both directions, which is why one worksheet mixes them.
Does the order of terms in a factored answer matter?
No. 6(2x + 3) and 6(3 + 2x) are equivalent, but the key uses the term order that matches the original expression to keep checking quick.