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
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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.
Teaching note 1
Expansion multiplies the outside factor by every term inside the grouping symbols.
Teaching note 2
Factoring reverses distribution by identifying a common factor shared by both terms.
Teaching note 3
Always verify a factored answer by distributing it back to the original expression.
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Frequently asked questions
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.