Distribute to Rewrite an Equivalent Expression

Supplied materials

• Paper and a pencil; drawing and spoken explanations are welcome. An adult may read directions and options aloud.
• Supplied worked-case record: Rewrite 5(x+4) as 5x+20.
• All quantities and shape descriptions are supplied in the worked example and questions; no purchase or personal information is needed.

Learn the idea

The distributive property multiplies each term in a sum by the outside factor. In reverse, a common factor can be taken out of a sum. Equivalent expressions preserve every term and are equal for all allowed inputs because the operation rule holds generally, not because one test happens to match.

Expand the supplied product by multiplying every grouped term. Record an equivalent expression, then check a sample input without treating that one example as the proof. Explain the distributive rule that guarantees the rewrite.

Multiply every term inside the group. Matching one chosen input alone does not prove two arbitrary expressions equivalent. Use an area model with two grouped widths or mark both distribution arrows.

1. Use an area model with two grouped widths or mark both distribution arrows.
2. Work through the supplied example and label what each number or attribute represents.
3. Expand the supplied product by multiplying every grouped term.
4. Answer the check, then try the three changed-input practice questions and explain one correction.

Check your reasoning

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Take it further

Factor 8x+24. Expected: 8(x+3).

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