Multiply out bracketsNumbers within 50
Name: Date:
Multiply out each bracket. Write the x-term and the number.
15(6 + 9x)x
24(8x − 12)x
33(x + 4)x
45(2 + 4x)x
58(x − 6)x
65(9x + 6)x
78(6 + 5x)x
84(2x + 4)x
Distributive property worksheets
Multiplying out a bracket means the number outside reaches everything inside it, not just the first thing. These free printable worksheets ask for the expanded form of expressions like 3(2x + 5), with the answer written as a coefficient and a constant.
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Distributive property
The answer key prints on a separate page.
What's on this sheet
The single most common mistake is stopping halfway: 3(2x + 5) becoming 6x + 5. Drawing two arcs from the 3 to each term inside makes the second multiplication impossible to forget, and it is worth doing on paper for a week rather than trusting it to memory.
Why this sheet works
Negatives are where it gets interesting. 4(2x − 3) is 8x − 12, and the minus travels with the 3 rather than staying behind. Some questions here carry a negative inside the bracket for exactly that reason, since a page of all-positive expansions teaches a rule that breaks the first time a real one appears.
How this one works
One question from this sheet, worked through a step at a time.
5(6 + 9x)
5(6 + 9x)
5 × 6=30
5 × 9x=45x
45x+30
- The 5 outside multiplies EVERYTHING inside the bracket, not just the thing next to it. Draw an arrow from the 5 to each of the two terms before working anything out — that is what stops one of them being left behind.
- First arrow: 5 × 6 = 30.
- Second arrow: 5 × 9x = 45x.
- Put the two together: 45x + 30. Check it by putting a small number in for x on both forms — they should agree, because they are the same amount written two ways.