Expanding Double Brackets
Expand products of two or more binomials, e.g., (x + 3)(x - 2) = x² + x - 6, using the grid method or FOIL; simplify the result by collecting like terms
Share and support
Teaching Table
Set out your lesson
Use a four-product grid to expand two linear brackets, then collect like terms.
First complete Expanding Single Brackets. Ask the learner to say what x² means and to simplify 2x + 3x. Expect x × x and 5x. Remind them that x² and x are different kinds of term. Revisit the prior lesson if signed products or distribution still need support.
Check readiness directly. Prerequisite availability is not attainment.
Start with the readiness check. Use Show, then Guided, then a fresh Try. These linked lessons may need several short sessions; do not impose a speed target. Read the active sheet on screen and answer on plain paper or by typing. No printer, cutting, purchase or internet is needed. The adult may read the exact prompt. Record any hints, scribing or calculation help. Oral explanations are allowed but do not show independent reading or handwriting. Use as much space and time as needed; pause or split the lesson. Keep this adult guide and all keys private. Share only the active learner sheet. Before Try, put Show, Guided work and notes aside. Keep the fresh Try givens available. Give no answer or target method during the first attempt. If help is needed, give it and mark the attempt supported. Review the key after the attempt. Record the actual response and help; do not invent success or infer mastery from one attempt. These are fictional paper or oral mathematics tasks. No personal information, public sharing, purchase, physical experiment or real measurement is required.
Record the actual response and assistance. These tasks do not establish mastery.
Use the complete materials on screen or print only the current sheet. Keep adult guidance out of learner view. Retain an earlier model only when the current step supplies it as context.
Teaching limits and safe use
These are finite task opportunities, not proof of mastery. Record what was attempted and what support was used.
Only products of two monic or negative-monic linear binomials are used. Three or more binomials and general leading coefficients are not taught.
Record the actual response and assistance. These tasks do not establish mastery.
Compare teaching approaches
Teaching approaches
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1 approach
Use a four-product grid to expand two linear brackets, then collect like terms.
Use a four-product grid to expand two linear brackets, then collect like terms.
Family records and proof options
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Learning resources
External links for extra practice. They do not replace Gakuva’s teaching approach.
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Check understanding
- Expand the product of two binomials using a systematic method (grid or FOIL)
- Collect like terms after expansion to simplify the result
- Expand products involving negative terms correctly
“Can your child multiply out two brackets like (x + 3)(x − 2) and collect the terms to get x² + x − 6?”
Curriculum record
- Type
- Procedural
- Subject
- Mathematics
- Domain
- Algebra
- Age range
- Ages 13–14
Standards