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Brackets","calculatorUse":null,"isCalculation":true,"parts":[{"id":"0fd02bb4-dc98-4019-81c1-49ef5c90fd3d","label":"0","content":"Expand and Simplify $(x - 2)(3x + 2)(x + 5)$","markscheme":"- Expands two brackets correctly, e.g., $(3x^2 + 17x + 10)$ or $(3x^2 - 4x - 4)$ M1\n- Multiplies by the third bracket M1\n- Final simplified expression $3x^3 + 11x^2 - 24x - 20$ A1","marks":3,"order":0,"markingRubric":{"totalMarks":3,"points":[{"id":"p1","marks":1,"description":"Correctly expands any two brackets to a quadratic.","code":"M"},{"id":"p2","marks":1,"description":"Multiplies the quadratic by the remaining linear bracket.","code":"M"},{"id":"p3","marks":1,"description":"Final simplified answer $3x^3 + 11x^2 - 24x - 20$.","code":"A"}],"finalAnswers":["3x^3 + 11x^2 - 24x - 20"],"generatedAt":"2026-05-07T02:01:01.511Z","modelVersion":"gemini-3-flash-preview"},"tableImages":[],"explanation":null,"options":[]}],"options":[],"explanation":null,"firstAttemptFullMarks":null,"walkthroughVideo":null},{"id":"88d03f80-e249-4b37-a6f7-b0e553166a40","revisionId":"e2a50f36-1fbd-4fd9-992c-abc40b1d8241","questionNumber":"10","questionType":"LA","specification":"","difficulty":2,"difficultyBand":"medium","tier":null,"totalMarks":3,"sourceTitle":"Expanding Triple Brackets","calculatorUse":null,"isCalculation":true,"parts":[{"id":"4876ee60-3045-41b4-b5e7-3d9918f00848","label":"0","content":"Expand and Simplify $(3x + 1)(x + 2)(x - 4)$","markscheme":"- Expands two brackets correctly, e.g., $(x^2 - 2x - 8)$ or $(3x^2 + 7x + 2)$ M1\n- Multiplies by the third bracket M1\n- Final simplified expression $3x^3 - 5x^2 - 26x - 8$ A1","marks":3,"order":0,"markingRubric":{"totalMarks":3,"points":[{"id":"p1","marks":1,"description":"Correctly expands any two brackets to a quadratic.","code":"M"},{"id":"p2","marks":1,"description":"Multiplies the quadratic by the remaining linear bracket.","code":"M"},{"id":"p3","marks":1,"description":"Final simplified answer $3x^3 - 5x^2 - 26x - 8$.","code":"A"}],"finalAnswers":["3x^3 - 5x^2 - 26x - 8"],"generatedAt":"2026-05-07T02:01:01.511Z","modelVersion":"gemini-3-flash-preview"},"tableImages":[],"explanation":{"methods":[{"id":"successive-expansion","label":"Expand brackets successively","steps":[{"type":"text","order":0,"title":"Expand the first pair","content":"Start with the last two brackets. Multiply each term in $(x+2)$ by each term in $(x-4)$:\n\n$$(x+2)(x-4)=x^2-4x+2x-8=x^2-2x-8$$\n\nSo the original product becomes\n\n$$(3x+1)(x+2)(x-4)=(3x+1)(x^2-2x-8).$$\n\nThis correct expansion of two brackets earns the first method mark (M1).","highlights":[{"text":"(x + 2)(x - 4)","location":"specification"}]},{"type":"text","order":1,"title":"Multiply and collect","content":"Multiply the quadratic by both terms in $(3x+1)$, then collect like terms:\n\n$$(3x+1)(x^2-2x-8)=3x^3-6x^2-24x+x^2-2x-8$$\n\n$$=3x^3-5x^2-26x-8$$\n\nThis is multiplication by the third bracket, earning the second method mark (M1)."},{"type":"text","order":2,"title":"State the final answer","content":"Therefore,\n\n$$\\boxed{3x^3-5x^2-26x-8}$$\n\nThis fully simplified expression earns the final accuracy mark (A1)."}]}],"generatedAt":"2026-09-01T09:17:43.436Z","modelVersion":"gpt-5.6-terra+diagrams-2","explanationVersion":"v3"},"options":[]}],"options":[],"explanation":{"methods":[{"id":"4876ee60-3045-41b4-b5e7-3d9918f00848:successive-expansion","label":"Expand brackets successively","steps":[{"type":"text","order":0,"title":"Expand the first pair","content":"Start with the last two brackets. Multiply each term in $(x+2)$ by each term in $(x-4)$:\n\n$$(x+2)(x-4)=x^2-4x+2x-8=x^2-2x-8$$\n\nSo the original product becomes\n\n$$(3x+1)(x+2)(x-4)=(3x+1)(x^2-2x-8).$$\n\nThis correct expansion of two brackets earns the first method mark (M1).","highlights":[{"text":"(x + 2)(x - 4)","location":"specification"}]},{"type":"text","order":1,"title":"Multiply and collect","content":"Multiply the quadratic by both terms in $(3x+1)$, then collect like terms:\n\n$$(3x+1)(x^2-2x-8)=3x^3-6x^2-24x+x^2-2x-8$$\n\n$$=3x^3-5x^2-26x-8$$\n\nThis is multiplication by the third bracket, earning the second method mark (M1)."},{"type":"text","order":2,"title":"State the final answer","content":"Therefore,\n\n$$\\boxed{3x^3-5x^2-26x-8}$$\n\nThis fully simplified expression earns the final accuracy mark (A1)."}]}],"generatedAt":"2026-09-01T09:17:46.686Z","modelVersion":"gpt-5.6-sol+diagrams-2","explanationVersion":"v3"},"firstAttemptFullMarks":null,"walkthroughVideo":null}],"subjectCode":"igcse_maths__oxford_aqa","summaries":[{"id":"64df4672-97ef-49d3-b8f4-76fec52a2de0","difficultyBand":"medium","calculatorUse":null,"totalMarks":3,"questionType":"LA","isCalculation":true},{"id":"4bc64585-6eb9-4a8f-b764-ab56a3d6130e","difficultyBand":"medium","calculatorUse":null,"totalMarks":3,"questionType":"LA","isCalculation":true},{"id":"78f75685-fcb2-4bff-a809-54d392f9efea","difficultyBand":"medium","calculatorUse":null,"totalMarks":3,"questionType":"LA","isCalculation":true},{"id":"354889bd-222b-4947-b54b-528370558cd9","difficultyBand":"medium","calculatorUse":null,"totalMarks":3,"questionType":"LA","isCalculation":true},{"id":"0fd7b290-efd6-4943-96c7-0856f8590076","difficultyBand":"medium","calculatorUse":null,"totalMarks":3,"questionType":"LA","isCalculation":true},{"id":"8fe72371-59f3-44b6-9690-13451b80b444","difficultyBand":"medium","calculatorUse":null,"totalMarks":3,"questionType":"LA","isCalculation":true},{"id":"bb22e8bb-f94a-4614-a71f-aeabd147d1d5","difficultyBand":"medium","calculatorUse":null,"totalMarks":3,"questionType":"LA","isCalculation":true},{"id":"43fccfe1-09e4-4c0c-91d8-d4a6d3232863","difficultyBand":"medium","calculatorUse":null,"totalMarks":3,"questionType":"LA","isCalculation":true},{"id":"2fdef4b0-1217-4b8d-aba4-596aa5cc5d97","difficultyBand":"medium","calculatorUse":null,"totalMarks":3,"questionType":"LA","isCalculation":true},{"id":"88d03f80-e249-4b37-a6f7-b0e553166a40","difficultyBand":"medium","calculatorUse":null,"totalMarks":3,"questionType":"LA","isCalculation":true},{"id":"ca392bc2-3d0b-4ba7-b0d5-81d9b5790693","difficultyBand":"medium","calculatorUse":null,"totalMarks":3,"questionType":"LA","isCalculation":true},{"id":"9f293ed4-1f33-4831-83e2-f7ac1340982c","difficultyBand":"medium","calculatorUse":null,"totalMarks":3,"questionType":"LA","isCalculation":true},{"id":"361fff12-8aa1-4e7c-8bb6-1f071bed0bcc","difficultyBand":"medium","calculatorUse":null,"totalMarks":3,"questionType":"LA","isCalculation":true},{"id":"4d6510f2-d4bb-4bce-bfd8-290ae3662f18","difficultyBand":"medium","calculatorUse":null,"totalMarks":3,"questionType":"LA","isCalculation":true}],"title":"Expanding Triple Brackets","topicId":"ab12d12d-260e-4889-9123-0582ebb0c140","topicSidebar":"$L3c","topicSlug":"grade-6-6-4-expanding-triple-brackets","topicTitle":"Expanding Triple Brackets"}]}],"$L3d","$L3e"]}]