cket M1\n- Final simplified expression $x^3 + 5x^2 - 16x - 80$ 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 $x^3 + 5x^2 - 16x - 80$.","code":"A"}],"finalAnswers":["x^3 + 5x^2 - 16x - 80"],"generatedAt":"2026-05-07T02:01:01.511Z","modelVersion":"gemini-3-flash-preview"},"explanation":{"methods":[{"id":"expand_first_pair","label":"Expand the first two brackets","steps":[{"type":"hyper_latex","block":{"nodes":[{"latex":"\\htmlData{anchor=start}{\\color{@sky}{(x+4)(x+5)}}"},{"latex":"\\htmlData{anchor=expanded}{x^2+5x+4x+20}"},{"latex":"\\htmlData{anchor=quadratic}{\\color{@green}{x^2+9x+20}}"}],"highlights":[{"color":"green","style":"text-color-with-background","anchor":"quadratic"}],"connections":[{"to":"expanded","from":"start","color":"sky","label":"multiply out"},{"to":"quadratic","from":"expanded","color":"green","label":"collect like terms"}]},"order":0,"title":"Expand and collect","description":"Multiply each term in the first bracket by each term in the second, then collect like terms. This correct quadratic expansion earns the first method mark (M1)."},{"type":"hyper_latex","block":{"nodes":[{"latex":"\\htmlData{anchor=product}{\\color{@sky}{(x^2+9x+20)(x-4)}}"},{"latex":"\\htmlData{anchor=distributed}{\\color{@orange}{x^3+9x^2+20x-4x^2-36x-80}}"}],"highlights":[{"color":"orange","style":"text-color-with-background","anchor":"distributed"}],"connections":[{"to":"distributed","from":"product","color":"orange","label":"distribute"}]},"order":1,"title":"Distribute the final bracket","description":"Now multiply each term of the quadratic by each term of the final bracket. This complete distribution earns the second method mark (M1)."},{"type":"hyper_latex","block":{"nodes":[{"latex":"\\htmlData{anchor=terms}{x^3+\\color{@amber}{9x^2-4x^2}+\\color{@teal}{20x-36x}-80}"},{"latex":"\\htmlData{anchor=answer}{\\color{@green}{x^3+5x^2-16x-80}}"}],"highlights":[{"color":"green","style":"text-color-with-background","anchor":"answer"}],"connections":[{"to":"answer","from":"terms","color":"green","label":"collect like terms"}]},"order":2,"title":"Collect like terms","description":"Combine the terms with the same power of x. The fully simplified expression earns the accuracy mark (A1)."}]}],"generatedAt":"2026-07-21T04:14:55.249Z","modelVersion":"gpt-5.6-terra","explanationVersion":"v3"},"options":[]}],"options":[],"explanation":null,"firstAttemptFullMarks":null},{"id":"0fd7b290-efd6-4943-96c7-0856f8590076","revisionId":"733b5d2f-c083-49fa-a5eb-170f0a4b6b4a","questionNumber":"5","questionType":"LA","specification":"","difficulty":2,"difficultyBand":null,"totalMarks":3,"sourceTitle":"Expanding Triple Brackets","calculatorUse":null,"parts":[{"id":"347cb4f9-0dc4-4690-baa4-eb7522fd3e7c","label":"0","content":"Expand and Simplify $(x + 3)(x - 1)^2$","markscheme":"- Expands $(x - 1)^2$ correctly to $(x^2 - 2x + 1)$ M1\n- Multiplies by $(x + 3)$ M1\n- Final simplified expression $x^3 + x^2 - 5x + 3$ A1","marks":3,"order":0,"markingRubric":{"totalMarks":3,"points":[{"id":"p1","marks":1,"description":"Correctly expands the squared bracket to $x^2 - 2x + 1$.","code":"M"},{"id":"p2","marks":1,"description":"Multiplies the quadratic by $(x + 3)$ with at least 4 terms correct.","code":"M"},{"id":"p3","marks":1,"description":"Final simplified answer $x^3 + x^2 - 5x + 3$.","code":"A"}],"finalAnswers":["x^3 + x^2 - 5x + 3"],"generatedAt":"2026-05-07T02:01:01.511Z","modelVersion":"gemini-3-flash-preview"},"explanation":{"methods":[{"id":"expand_then_multiply","label":"Expand then multiply","steps":[{"type":"hyper_latex","block":{"nodes":[{"latex":"(x-1)^2=(x-1)(x-1)"},{"latex":"(x-1)(x-1)=x^2-x-x+1"},{"latex":"x^2-x-x+1=x^2-2x+1"}]},"order":1,"title":"Expand the square","description":"Treat

Expanding Triple Brackets Questions

Expanding Triple Brackets Questions

Expanding Triple Brackets Questions

Expanding Triple Brackets Questions