What you’ll learn
Rewrite expressions to reveal meaning.
Key idea
Distribution can show repeated groups; factoring can show a shared amount. The algebraic value stays the same, but the structure highlights different information.
Suppose a fundraiser sells three standard bundles with x items each and two upgraded bundles with x items plus five extras each. The total 3x + 2(x + 5) can be rewritten as 5x + 10: five groups of x items and ten extra items. The second form makes the total number of each kind visible.
Worked example
Enter the exact value or ordered values in the format requested below.
There are 3 bundles. Each contains an item costing x dollars and packaging costing $8. Create a factored total-cost model revealing repeated bundle cost.
- Each bundle costs x+8 dollars including its own packaging.
- For 3 bundles total=3(x+8)=3x+24; the factor 3 reveals 3 copies of the entire bundle.
Answer: 3(x+8)
Quick Check
Choose which candidate representation satisfies the requirements of 'Rewrite expressions to reveal meaning' and justify the choice.
For 7 bundles each costing x+1, compare A=7(x+1), B=7x+1, C=x+7. Select the all-input model with a property-based justification.