// Numbas version: finer_feedback_settings
{"name": "Polynomials: Expand and Simplify 2a", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"name": "Polynomials: Expand and Simplify 2a", "tags": [], "metadata": {"description": "<p>Finding the product of two linear functions of the form $mx+c$.</p>", "licence": "Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International"}, "statement": "<p>Given two functions, \\[ f(x) = \\simplify{{b1}x+{c1}}, \\quad g(x)=\\simplify{{b2}x+{c2}}\\]</p>\n<p>calculate the product \\[\\simplify{f(x)g(x)}.\\]</p>", "advice": "<p>For the functions \\[ f(x) = \\simplify{{b1}x+{c1}}, \\quad g(x)=\\simplify{{b2}x+{c2}},\\] their product is&nbsp;</p>\n<p>\\[ \\begin{split} f(x) g(x) &amp;\\,= \\left(\\simplify{{b1}x+{c1}}\\right)\\left(\\simplify{{b2}x+{c2}}\\right) \\\\ &amp;\\,= \\simplify{{b1}x({b2}x+{c2}) +{c1}({b2}x+{c2})}. \\end{split} \\]</p>\n<p>Expanding each bracket and collecting similar terms:</p>\n<p>\\[ \\begin{split} f(x) g(x)&nbsp; &amp;\\,= \\simplify{{b1}x({b2}x+{c2}) +{c1}({b2}x+{c2})} \\\\ &amp;\\,=\\simplify[all,!cancelTerms,!collectNumbers]{{b1*b2}x^2+{b1*c2}x+{c1*b2}x+{c1*c2}} \\\\&nbsp;&amp;\\,=\\simplify{{b1*b2}x^2+{b1*c2}x+{c1*b2}x+{c1*c2}} \\end{split} \\]</p>", "rulesets": {}, "extensions": [], "builtin_constants": {"e": true, "pi,\u03c0": true, "i": true}, "constants": [], "variables": {"b1": {"name": "b1", "group": "Ungrouped variables", "definition": "random(1..8)", "description": "", "templateType": "anything", "can_override": false}, "b2": {"name": "b2", "group": "Ungrouped variables", "definition": "random(1..5 except b1)", "description": "", "templateType": "anything", "can_override": false}, "c1": {"name": "c1", "group": "Ungrouped variables", "definition": "random(-10..10 except [0,1,-1])", "description": "", "templateType": "anything", "can_override": false}, "c2": {"name": "c2", "group": "Ungrouped variables", "definition": "random(-10..10 except 0)", "description": "", "templateType": "anything", "can_override": false}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["b1", "c1", "b2", "c2"], "variable_groups": [], "functions": {}, "preamble": {"js": "", "css": ""}, "parts": [{"type": "jme", "useCustomName": false, "customName": "", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "answer": "{b1*b2}x^2+({b1*c2}+{c1*b2})x+{c1*c2}", "showPreview": true, "checkingType": "absdiff", "checkingAccuracy": 0.001, "failureRate": 1, "vsetRangePoints": 5, "vsetRange": [0, 1], "checkVariableNames": false, "singleLetterVariables": false, "allowUnknownFunctions": true, "implicitFunctionComposition": false, "caseSensitive": false, "mustmatchpattern": {"pattern": "$n`?x^2+`+-$n`?*x+`+-$n`?", "partialCredit": 0, "message": "", "nameToCompare": ""}, "valuegenerators": [{"name": "x", "value": ""}]}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always", "type": "question", "contributors": [{"name": "Ruth Hand", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/3228/"}, {"name": "Ben McGovern", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/4872/"}]}]}], "contributors": [{"name": "Ruth Hand", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/3228/"}, {"name": "Ben McGovern", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/4872/"}]}