// Numbas version: finer_feedback_settings
{"name": "Expand product of brackets", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"variable_groups": [], "variables": {"b": {"templateType": "anything", "group": "Ungrouped variables", "definition": "random(-9..9 except [0,a])", "description": "", "name": "b"}, "d": {"templateType": "anything", "group": "Ungrouped variables", "definition": "random(-9..9 except [0,c])", "description": "", "name": "d"}, "a": {"templateType": "anything", "group": "Ungrouped variables", "definition": "random(-5..5 except 0)", "description": "", "name": "a"}, "c": {"templateType": "anything", "group": "Ungrouped variables", "definition": "random(-5..5 except 0)", "description": "", "name": "c"}}, "ungrouped_variables": ["a", "c", "b", "d"], "question_groups": [{"pickingStrategy": "all-ordered", "questions": [], "name": "", "pickQuestions": 0}], "name": "Expand product of brackets", "functions": {}, "showQuestionGroupNames": false, "parts": [{"showCorrectAnswer": true, "marks": 0, "scripts": {}, "gaps": [{"answer": "{a*c}x^2+{b*c+a*d}x+{b*d}", "musthave": {"message": "<p>Input your answer as a quadratic in $x$, in the form $ax^2+bx+c$ for appropriate integers $a,\\;b,\\;c$.</p>", "showStrings": false, "partialCredit": 0, "strings": ["x^2"]}, "vsetrange": [0, 1], "checkingaccuracy": 0.001, "answersimplification": "std", "expectedvariablenames": [], "notallowed": {"message": "<p>Do not include brackets in your answer. Input your answer as a quadratic in $x$, in the form $ax^2+bx+c$ for appropriate integers $a,\\;b,\\;c$.</p>", "showStrings": false, "partialCredit": 0, "strings": ["("]}, "showpreview": true, "maxlength": {"length": "0", "message": "<p>Input your answer as a quadratic in $x$, in the form $ax^2+bx+c$ for appropriate integers $a,\\;b,\\;c$.</p>", "partialCredit": 0}, "checkingtype": "absdiff", "scripts": {}, "checkvariablenames": false, "type": "jme", "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "variableReplacements": [], "marks": 2, "vsetrangepoints": 5}], "type": "gapfill", "prompt": "<p>$\\simplify[std]{({a}x+{b})({c}x+{d})}=\\;$[[0]].</p>\n<p>Your answer should be a quadratic in $x$ and should not include any brackets.</p>\n<p>You can click on \"Show steps\" for more information, but you will lose one mark if you do so.</p>", "steps": [{"prompt": "<p>There are many ways to expand an expression such as $(ax+b)(cx+d)$.</p>\n<p>One way:</p>\n<p>\\[\\begin{eqnarray*} (ax+b)(cx+d)&amp;=&amp;ax(cx+d)+b(cx+d)\\\\&amp;=&amp;acx^2+adx+bcx+bd\\\\&amp;=&amp;acx^2+(ad+bc)x+bd\\end{eqnarray*}\\]</p>", "scripts": {}, "type": "information", "showCorrectAnswer": true, "variableReplacementStrategy": "originalfirst", "variableReplacements": [], "marks": 0}, {"prompt": "<p><iframe height=\"480\" src=\"https://player.vimeo.com/video/8169375\" frameborder=\"0\" width=\"640\" allowfullscreen=\"\" mozallowfullscreen=\"\" webkitallowfullscreen=\"\"></iframe></p>", "scripts": {}, "type": "information", "showCorrectAnswer": true, "variableReplacementStrategy": "originalfirst", "variableReplacements": [], "marks": 0}], "variableReplacementStrategy": "originalfirst", "variableReplacements": [], "stepsPenalty": 1}], "statement": "<p>Expand the following to give a quadratic in $x$.</p>", "tags": ["ACC1012", "acc1012", "algebra", "algebraic manipulation", "checked2015", "expansion of brackets", "expansion of the product of two linear terms"], "rulesets": {"std": ["all", "!noLeadingMinus", "!collectNumbers"]}, "preamble": {"css": "", "js": ""}, "type": "question", "metadata": {"notes": "\n\t\t    \t\t        \t\t    \t\t    \t\t<p><strong>15/08/2012:</strong></p>\n\t\t    \t\t        \t\t    \t\t    \t\t                <p>Added tags.</p>\n\t\t    \t\t        \t\t    \t\t    \t\t                <p>Added description.</p>\n\t\t    \t\t        \t\t    \t\t    \n\t\t    \t\t        \t\t    \n\t\t    \t\t        \n\t\t    \n\t\t", "licence": "Creative Commons Attribution 4.0 International", "description": "<p>Expand $(ax+b)(cx+d)$.</p>"}, "variablesTest": {"condition": "", "maxRuns": 100}, "advice": "\n\t  <p>Using the method given by Show steps we have:</p>\n\t  <p>\\[\\begin{eqnarray*}\\simplify[std]{ ({a}x+{b})({c}x+{d})}&amp;=&amp;\\simplify[std]{{a}x*({c}x+{d})+{b}({c}x+{d})}\\\\&amp;=&amp;\\simplify[std]{{a*c}x^2+{a*d}x+{b*c}x+{b*d}}\\\\&amp;=&amp;\\simplify[std]{{a*c}x^2+{(a*d+b*c)}x+{b*d}}\\end{eqnarray*}\\]</p>\n\t  <p>&nbsp;</p>\n\t  \n\t    \n\t  \n\t  \n\t", "contributors": [{"name": "Newcastle University Mathematics and Statistics", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/697/"}]}]}], "contributors": [{"name": "Newcastle University Mathematics and Statistics", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/697/"}]}