racket M1\n- Fully correct simplification to reach $6x^3 + 25x^2 + 2x - 8$ A1","marks":3,"order":0,"markingRubric":{"totalMarks":3,"points":[{"id":"p1","marks":1,"description":"Expands any two of the three brackets correctly into a quadratic expression.","code":"M","acceptable":["6x^2 + x - 2","2x^2 + 7x - 4","3x^2 + 14x + 8"]},{"id":"p2","marks":1,"description":"Multiplies their quadratic result by the remaining linear bracket.","code":"M"},{"id":"p3","marks":1,"description":"Fully correct expansion and simplification to reach the given cubic expression.","code":"A"}],"finalAnswers":[],"generatedAt":"2026-05-06T14:00:50.739Z","modelVersion":"gemini-3-flash-preview"},"explanation":{"methods":[{"id":"expand_in_stages","label":"Expand in stages","steps":[{"type":"hyper_latex","block":{"nodes":[{"latex":"$$(3x+2)(2x-1)(x+4)=\\htmlData{anchor=expanded_pair}{\\color{@sky}{(6x^2-3x+4x-2)(x+4)}}$"},{"latex":"$$(3x+2)(2x-1)(x+4)=\\htmlData{anchor=collected_pair}{\\color{@sky}{(6x^2+x-2)(x+4)}}$"}],"connections":[{"to":"collected_pair","from":"expanded_pair","color":"sky","label":"collect like terms"}]},"order":1,"title":"Expand two brackets","description":"Start by expanding the first two brackets, keeping the third bracket unchanged. Reaching the quadratic earns the first M1 mark."},{"type":"hyper_latex","block":{"nodes":[{"latex":"$$(6x^2+x-2)(x+4)=\\htmlData{anchor=distributed}{\\color{@orange}{6x^2(x+4)+x(x+4)-2(x+4)}}$"},{"latex":"$$(6x^2+x-2)(x+4)=\\htmlData{anchor=expanded_all}{\\color{@orange}{6x^3+24x^2+x^2+4x-2x-8}}$"}],"connections":[{"to":"expanded_all","from":"distributed","color":"orange","label":"expand each bracket"}]},"order":2,"title":"Multiply third bracket","description":"Distribute the third bracket across all three terms of the quadratic. Completing this multiplication earns the second M1 mark."},{"type":"hyper_latex","block":{"nodes":[{"latex":"$$(6x^2+x-2)(x+4)=\\htmlData{anchor=grouped}{\\color{@purple}{6x^3+(24x^2+x^2)+(4x-2x)-8}}$"},{"latex":"$$(6x^2+x-2)(x+4)=\\htmlData{anchor=result}{\\color{@purple}{6x^3+25x^2+2x-8}}$"}],"connections":[{"to":"result","from":"grouped","color":"purple","label":"add coefficients"}]},"order":3,"title":"Collect like terms","description":"Group terms with the same power, then add their coefficients. The fully correct result earns the A1 mark. This is the required right-hand side, so the identity holds for all values of x."}]}],"generatedAt":"2026-07-19T16:37:54.120Z","modelVersion":"gpt-5.6-sol","explanationVersion":"v3"},"options":[]}],"options":[],"explanation":null,"firstAttemptFullMarks":null},{"id":"f5b256be-46cb-4f45-ae2e-1537270ad749","revisionId":"f421af00-8343-4270-9e33-0d1eada3c17a","questionNumber":null,"questionType":"LA","specification":"","difficulty":1,"difficultyBand":"medium","totalMarks":3,"sourceTitle":null,"calculatorUse":"non_calc","parts":[{"id":"42ee2da8-4da6-4c31-b631-f2f0e04c7eb0","label":"a","content":"Expand and simplify $(x + 2)(x - 4)(3x + 1)$","markscheme":"- Expands two brackets to get $x^2 - 2x - 8$ or $3x^2 + 7x + 2$ or $3x^2 - 11x - 4$ M1\n- Multiplies the resulting quadratic by the third linear 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":"Evidence of expanding any two brackets correctly to a quadratic.","code":"M","acceptable":["x^2 - 2x - 8","3x^2 + 7x + 2","3x^2 - 11x - 4"]},{"id":"p2","marks":1,"description":"Multiplies their quadratic by the remaining linear bracket, allowing for at most two sign errors.","code":"M"},{"id":"p3","marks":1,"description":"Correct simplified cubic expression.","code":"A"}],"finalAnswers":[],"generatedAt":"2026-05-06T14:00:48.972Z","modelVersion":"gemini-3-flash-preview"},"explanation":{"methods":[{"id":"first_two_brackets","label":"Expand the first two brackets","steps":[{"type":"hyper_latex","block":{"nodes":[{"latex":"$$\\htmlData{anchor=pair}{\\color{@sky}{(x+2)(x-4)}}$"},{"latex":"$$\\htmlData{anchor=expan

Expanding Triple Brackets Questions

Expanding Triple Brackets Questions

Expanding Triple Brackets Questions

Expanding Triple Brackets Questions