// Numbas version: finer_feedback_settings
{"name": "Simplify Algebraic Expressions: 2 unknowns", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"functions": {}, "name": "Simplify Algebraic Expressions: 2 unknowns", "tags": ["algebra", "algebraic manipulation", "expanding brackets", "simplification", "simplifying an expression"], "advice": "\n  <p>Expanding the brackets we have:</p>\n    <p>\\[\\begin{eqnarray*}\\simplify[std]{({a}x+{b}y)({c}x+{d}y)-({a}x+{d}y)({c}x+{b}y)}&amp;=&amp;(\\simplify[std]{{a*c}x^2+{b*c+a*d}x*y+{b*d}y^2})-(\\simplify[std]{{a*c}x^2+{b*a+c*d}x*y+{b*d}y^2})\\\\&amp;=&amp;\\simplify[std]{{b*c+a*d}x*y-{b*a+c*d}x*y}\\\\&amp;=&amp;\\var{(a-c)*(d-b)}xy\\end{eqnarray*}\\]</p>\n  ", "rulesets": {"std": ["all", "!collectNumbers", "!noLeadingMinus"]}, "parts": [{"prompt": "\n      <p>Simplify:</p>\n        <p>$\\simplify[std]{({a}x+{b}y)({c}x+{d}y)-({a}x+{d}y)({c}x+{b}y)}=\\;$[[0]]</p>\n        <p>Do not include brackets in your answer.</p>\n        <p>Input $xy$ as $x*y$.</p>\n      ", "gaps": [{"notallowed": {"message": "<p>Do not include brackets in your answer.</p>", "showstrings": false, "strings": ["("], "partialcredit": 0.0}, "checkingaccuracy": 0.001, "vsetrange": [0.0, 1.0], "vsetrangepoints": 5.0, "checkingtype": "absdiff", "answersimplification": "std", "marks": 2.0, "answer": "{(a-c)*(d-b)}*x*y", "type": "jme", "maxlength": {"length": 7.0, "message": "<p>You can simplify the expression further.</p>", "partialcredit": 0.0}}], "type": "gapfill", "marks": 0.0}], "extensions": [], "statement": "<p>Simplify the following expression.</p>", "variable_groups": [], "progress": "ready", "type": "question", "variables": {"a": {"definition": "random(-6..6 except 0)", "name": "a"}, "c": {"definition": "random(-6..6 except [0,a])", "name": "c"}, "b": {"definition": "random(1..9 except a)", "name": "b"}, "d": {"definition": "random(1..9 except [c,b])", "name": "d"}}, "metadata": {"notes": "\n    \t\t    \t\t<p><strong>18/08/2012:</strong></p>\n    \t\t    \t\t        <p>Added tags.</p>\n    \t\t    \t\t        <p>Added description.</p>\n    \t\t    \n    \t\t", "description": "<p>Simplify $(ax+by)(cx+dy)-(ax+dy)(cx+by)$. Answer is a multiple of $xy$.</p>", "licence": "Creative Commons Attribution 4.0 International"}, "showQuestionGroupNames": false, "question_groups": [{"name": "", "pickingStrategy": "all-ordered", "pickQuestions": 0, "questions": []}], "contributors": [{"name": "Bill Foster", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/6/"}], "resources": []}]}], "contributors": [{"name": "Bill Foster", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/6/"}]}