Expand (x+a)(x+b)(x+c), where x is a randomised variable, and a,b,c are randomised integers.
\nNote that the pattern restriction in the marking checks that there are no brackets and that the expression is simplified to at most a single x^3, x^2, x and constant term; but it will let you get away with an additional -x^2 and/or -x term. (e.g., you could write 3x as 4x -x and the marking would accept this. This was to stop the pattern matching getting too complicated.
\nPart of HELM Book 1.3
", "licence": "Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International"}, "statement": "Practise these questions repeatedly until you are very confident at removing brackets.
", "advice": "\\[\\begin{align*} \\var{expression(q3expr)} &= \\left[( \\var{t[0]} )(\\var{t[1]})\\right]\\times(\\var{t[2]})\\\\ &=(\\var{te[0]})\\times(\\var{t[2]})\\\\ &= \\var{te[1]}\\\\ &=(\\var{te[2]})+(\\var{te[3]})\\\\&=\\var{q3ans} \\end{align*}\\]
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", "templateType": "anything", "can_override": false}, "te": {"name": "te", "group": "question 3", "definition": "[\nsimplify(expression(\"(\" + q3v + q3signs[0] + q3c[0] + \")(\" \n + q3v + q3signs[1] + q3c[1] + \")\"),\"expandBrackets,all\"),\nexpression( \n \"(\"+string(simplify(expression(\n \"(\" + q3v + q3signs[0] + q3c[0] + \")(\" \n + q3v + q3signs[1] + q3c[1] + \")\"\n ),\"expandBrackets,all\"))+\n \")*\"+q3v+\"+(\"+ string(simplify(expression(\n \"(\" + q3v + q3signs[0] + q3c[0] + \")(\" \n + q3v + q3signs[1] + q3c[1] + \")\"\n ),\"expandBrackets,all\"))+\n \")*\"+string(simplify(expression(\"(\"+q3signs[2] + q3c[2]+\")\"),\"all\"))\n ),\nsimplify(expression( \n \"(\"+string(simplify(expression(\n \"(\" + q3v + q3signs[0] + q3c[0] + \")(\" \n + q3v + q3signs[1] + q3c[1] + \")\"\n ),\"expandBrackets,all\"))+\n \")*\"+q3v\n ),[\"expandBrackets\",\"basic\",\"unitFactor\",\"unitPower\",\"zeroFactor\",\n \"zeroTerm\",\"zeroPower\",\"collectNumbers\",\"constantsFirst\",\n \"cancelFactors\"]),\nsimplify(expression(\n \"(\"+ string(simplify(expression(\n \"(\" + q3v + q3signs[0] + q3c[0] + \")(\" \n + q3v + q3signs[1] + q3c[1] + \")\"\n ),\"expandBrackets,all\"))+\n \")*\"+string(simplify(expression(\"(\"+q3signs[2] + q3c[2]+\")\"),\"all\")) \n ),[\"expandBrackets\",\"basic\",\"unitFactor\",\"unitPower\",\"zeroFactor\",\n \"zeroTerm\",\"zeroPower\",\"collectNumbers\",\"constantsFirst\",\n \"cancelFactors\"]) \n]", "description": "The terms, getting expanded, for display in the advice.
", "templateType": "anything", "can_override": false}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["alphabet"], "variable_groups": [{"name": "question 3", "variables": ["q3v", "q3c", "q3expr", "q3ans", "q3signs", "ve", "t", "te"]}], "functions": {}, "preamble": {"js": "", "css": ""}, "parts": [{"type": "jme", "useCustomName": true, "customName": "Exercise 3", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "Remove the brackets from $\\var{q3expr}$ and simplify.
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