Expand (a+b)(c+d). a,b,c,d are random terms that can be +ve or -ve, and can consist of a number and/or a letter.
\nThe answer must contain no brackets but will be accepted if it is not simplified from there.
\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{te[0]})(\\var{te[1]})&=(\\var{te[0]})\\times(\\var{te[1]})\\\\ &=(\\var{te[2]})(\\var{te[1]})+(\\var{te[3]})(\\var{te[1]}) \\\\ &=(\\var{te[4]})+(\\var{te[5]})\\\\&=\\var{q2ans} \\end{align*}\\]
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", "templateType": "anything", "can_override": false}, "q2signs": {"name": "q2signs", "group": "question 2", "definition": "[random(\"\",\"-\"),random(\"+\",\"-\"),random(\"\",\"-\"),random(\"+\",\"-\")]", "description": "", "templateType": "anything", "can_override": false}, "q2cstr": {"name": "q2cstr", "group": "question 2", "definition": "[string(q2c[0]),\n string(q2c[1]),\n if(q2c[2]=1,\"\",string(q2c[2])),\n if(q2c[3]=1,\"\",string(q2c[3]))\n ]", "description": "", "templateType": "anything", "can_override": false}, "q2v": {"name": "q2v", "group": "question 2", "definition": "shuffle(alphabet)[0..4]", "description": "", "templateType": "anything", "can_override": false}, "terms": {"name": "terms", "group": "question 2", "definition": "[[\"(\"+ q2signs[0] + q2cstr[0] + q2signs[1] + q2v[0] + \")\",\"(\" \n + q2signs[2] + q2cstr[1] + q2signs[3] + q2v[1]+\")\",\n q2signs[0] + q2cstr[0],\n q2signs[1] + q2v[0]\n ],\n [\"(\"+ q2signs[0] + q2cstr[2] + q2v[0] + q2signs[1] + q2cstr[0] + \")\",\"(\"\n + q2signs[2] + q2cstr[3] + q2v[0] + q2signs[3] + q2cstr[1] + \")\",\n q2signs[0] + q2cstr[2] + q2v[0],\n q2signs[1] + q2cstr[0]\n ],\n [\"(\"+ q2signs[0] + q2cstr[0] + q2signs[1] + q2cstr[2] + q2v[0] + \")\",\"(\" \n + q2signs[2] + q2cstr[3] + q2v[0] + q2signs[3] + q2cstr[1] + \")\",\n q2signs[0] + q2cstr[0],\n q2signs[1] + q2cstr[2] + q2v[0]\n ],\n [\"(\"+ q2signs[0] + q2cstr[2] + q2v[0] + q2signs[1] + q2cstr[0] + \")\",\"(\"\n + q2signs[2] + q2cstr[1] + q2signs[3] + q2cstr[3] + q2v[0] + \")\",\n q2signs[0] + q2cstr[2] + q2v[0],\n q2signs[1] + q2cstr[0]\n ],\n [\"(\"+ q2signs[0] + q2cstr[0] + q2signs[1] + q2cstr[2] + q2v[0] + \")\",\"(\"\n + q2signs[2] + q2cstr[1] + q2signs[3] + q2cstr[3] + q2v[0] + \")\",\n q2signs[0] + q2cstr[0],\n q2signs[1] + q2cstr[2] + q2v[0]\n ] \n ][q2idx]", "description": "for display in the advice
", "templateType": "anything", "can_override": false}, "te": {"name": "te", "group": "question 2", "definition": "[expression(terms[0]),\n expression(terms[1]),\n expression(terms[2]),\n expression(terms[3]),\n simplify(expression(\n \"(\"+string(expression(terms[2]))+\")*(\"+string(expression(terms[1]))+\")\"\n ),[\"expandBrackets\",\"basic\",\"unitFactor\",\"unitPower\",\"zeroFactor\",\n \"zeroTerm\",\"zeroPower\",\"collectNumbers\",\"constantsFirst\",\n \"cancelFactors\"]),\n simplify(expression(\n \"(\"+string(expression(terms[3]))+\")*(\"+string(expression(terms[1]))+\")\"\n ),[\"expandBrackets\",\"basic\",\"unitFactor\",\"unitPower\",\"zeroFactor\",\n \"zeroTerm\",\"zeroPower\",\"collectNumbers\",\"constantsFirst\",\n \"cancelFactors\"]),\n \n ]", "description": "the terms, done as expressions, for display in the advice.
", "templateType": "anything", "can_override": false}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["alphabet"], "variable_groups": [{"name": "question 2", "variables": ["q2idx", "q2signs", "q2c", "q2cstr", "q2v", "q2exprs", "q2expr", "q2ans", "terms", "te"]}], "functions": {}, "preamble": {"js": "", "css": ""}, "parts": [{"type": "jme", "useCustomName": true, "customName": "Exercise 2", "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 $\\var{q2expr}$ and simplify where possible.
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