1. Using the method given by Show steps we have:
\n\\[\\simplify[std]{ {a}x*({c}x+{d})}=\\simplify[std]{{a*c}x^2+{a*d}x}\\]
\n2.
\n\\[\\simplify[std]{ ({a1}x+{b1})*({c1}x)}=\\simplify[std]{{a1*c1}x^2+{b1*c1}x}\\]
\n\n
\n ", "rulesets": {"std": ["all", "!noLeadingMinus", "!collectNumbers"]}, "parts": [{"stepspenalty": 1.0, "prompt": "\n
$\\simplify[std]{({a}x)({c}x+{d})}=\\;$[[0]].
\n$\\simplify[std]{({a1}x+{b1})({c1}x)}=\\;$[[1]].
\nYour answers should be quadratics in $x$ and should not include any brackets.
\nYou can click on Show steps to get more information, but you will lose one mark if you do so.
\n ", "gaps": [{"notallowed": {"message": "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 $a,\\;b,\\;c$.
", "showstrings": false, "strings": ["("], "partialcredit": 0.0}, "checkingaccuracy": 0.001, "vsetrange": [0.0, 1.0], "vsetrangepoints": 5.0, "checkingtype": "absdiff", "answersimplification": "std", "marks": 1.0, "answer": "{a*c}x^2+{a*d}x", "type": "jme", "maxlength": {"length": 13.0, "message": "Input your answer as a quadratic in $x$, in the form $ax^2+bx+c$ for appropriate integers $a,\\;b,\\;c$.
", "partialcredit": 0.0}}, {"notallowed": {"message": "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 $a,\\;b,\\;c$.
", "showstrings": false, "strings": ["("], "partialcredit": 0.0}, "checkingaccuracy": 0.001, "vsetrange": [0.0, 1.0], "vsetrangepoints": 5.0, "checkingtype": "absdiff", "answersimplification": "std", "marks": 1.0, "answer": "{a1*c1}*x^2+{b1*c1}*x", "type": "jme", "maxlength": {"length": 13.0, "message": "Input your answer as a quadratic in $x$, in the form $ax^2+bx+c$ for appropriate integers $a,\\;b,\\;c$.
", "partialcredit": 0.0}}], "steps": [{"prompt": "\\[ax(cx+d)=acx^2+adx\\]
", "type": "information", "marks": 0.0}], "marks": 0.0, "type": "gapfill"}], "statement": "Expand the following to give quadratics in $x$.
", "variable_groups": [], "progress": "ready", "type": "question", "variables": {"a": {"definition": "random(-5..5 except 0)", "name": "a"}, "c": {"definition": "random(-5..5 except 0)", "name": "c"}, "b": {"definition": 0.0, "name": "b"}, "d": {"definition": "random(-9..9 except [0,c])", "name": "d"}, "a1": {"definition": "random(-5..5 except [0,a])", "name": "a1"}, "b1": {"definition": "random(-9..9 except [0,c])", "name": "b1"}, "c1": {"definition": "random(-5..5 except 0)", "name": "c1"}}, "metadata": {"notes": "\n \t\t \t\t15/08/2012:
\n \t\t \t\tAdded tags.
\n \t\t \t\tAdded description.
\n \t\t \n \t\t", "description": "Expand $ax(cx+d)$ and expand $(rx+s)(px)$
", "licence": "Creative Commons Attribution 4.0 International"}, "showQuestionGroupNames": false, "question_groups": [{"name": "", "pickingStrategy": "all-ordered", "pickQuestions": 0, "questions": []}]}, {"name": "Expansion of two brackets: Linear 2", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Bill Foster", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/6/"}], "functions": {}, "tags": ["algebra", "algebraic manipulation", "expansion of brackets", "expansion of the product of two linear terms"], "advice": "\nUsing the method given by Show steps we have:
\n\\[\\begin{eqnarray*}\\simplify[std]{ ({a}x+{b})({c}x+{d})}&=&\\simplify[std]{{a}x*({c}x+{d})+{b}({c}x+{d})}\\\\&=&\\simplify[std]{{a*c}x^2+{a*d}x+{b*c}x+{b*d}}\\\\&=&\\simplify[std]{{a*c}x^2+{(a*d+b*c)}x+{b*d}}\\end{eqnarray*}\\]
\n\n ", "rulesets": {"std": ["all", "!noLeadingMinus", "!collectNumbers"]}, "parts": [{"stepspenalty": 1.0, "prompt": "\n
$\\simplify[std]{({a}x+{b})({c}x+{d})}=\\;$[[0]].
\nYour answer should be a quadratic in $x$ and should not include any brackets.
\nYou can click on Show steps for more information, but you will lose one mark if you do so.
\n ", "gaps": [{"notallowed": {"message": "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 $a,\\;b,\\;c$.
", "showstrings": false, "strings": ["("], "partialcredit": 0.0}, "checkingaccuracy": 0.001, "vsetrange": [0.0, 1.0], "vsetrangepoints": 5.0, "checkingtype": "absdiff", "answersimplification": "std", "maxlength": {"length": 17.0, "message": "Input your answer as a quadratic in $x$, in the form $ax^2+bx+c$ for appropriate integers $a,\\;b,\\;c$.
", "partialcredit": 0.0}, "answer": "{a*c}x^2+{b*c+a*d}x+{b*d}", "marks": 2.0, "type": "jme", "musthave": {"message": "Input your answer as a quadratic in $x$, in the form $ax^2+bx+c$ for appropriate integers $a,\\;b,\\;c$.
", "showstrings": false, "strings": ["x^2"], "partialcredit": 0.0}}], "steps": [{"prompt": "\nThere are many ways to expand an expression such as $(ax+b)(cx+d)$.
\nOne way:
\n\\[\\begin{eqnarray*} (ax+b)(cx+d)&=&ax(cx+d)+b(cx+d)\\\\&=&acx^2+adx+bcx+bd\\\\&=&acx^2+(ad+bc)x+bd\\end{eqnarray*}\\]
\n ", "type": "information", "marks": 0.0}], "marks": 0.0, "type": "gapfill"}], "statement": "Expand the following to give a quadratic in $x$.
", "variable_groups": [], "progress": "ready", "type": "question", "variables": {"a": {"definition": "random(-5..5 except 0)", "name": "a"}, "c": {"definition": "random(-5..5 except 0)", "name": "c"}, "b": {"definition": "random(-9..9 except [0,a])", "name": "b"}, "d": {"definition": "random(-9..9 except [0,c])", "name": "d"}}, "metadata": {"notes": "\n \t\t15/08/2012:
\n \t\tAdded tags.
\n \t\tAdded description.
\n \t\t", "description": "Expand $(ax+b)(cx+d)$.
", "licence": "Creative Commons Attribution 4.0 International"}, "showQuestionGroupNames": false, "question_groups": [{"name": "", "pickingStrategy": "all-ordered", "pickQuestions": 0, "questions": []}]}, {"name": "Expansion of two brackets: Linear and Quadratic ", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Bill Foster", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/6/"}], "functions": {}, "tags": ["algebra", "algebraic manipulation", "expansion of a quadratic and linear term", "expansion of brackets"], "advice": "\nUsing the method given by Show steps:
\n\\[\\begin{eqnarray*}\\simplify[std]{ ({p}w+{q})({a}w^2+{b}w+{c})}&=&\\simplify[std]{{p}w*({a}w^2+{b}w+{c})+{q}({a}w^2+{b}w+{c})}\\\\&=&\\simplify[std]{{a*p}w^3+{b*p}w^2+{c*p}w+{a*q}w^2+{q*b}w+{c*q}}\\\\&=&\\simplify[std]{{a*p}w^3+{(a*q+b*p)}w^2+{b*q+c*p}w+{c*q}}\\end{eqnarray*}\\]
\n\n ", "rulesets": {"std": ["all", "!noLeadingMinus", "!collectNumbers"]}, "parts": [{"stepspenalty": 1.0, "prompt": "\n
$\\simplify[std]{({p}w+{q})({a}w^2+{b}w+{c})}=\\;$[[0]].
\nYour answer should be a cubic in $w$ and should not include any brackets.
\nYou can click on Show steps for more information, but you will lose one mark if you do so.
\n ", "gaps": [{"notallowed": {"message": "Do not include brackets in your answer. Input your answer as a cubic in $w$, in the form $aw^3+bw^2+cw+d$ for appropriate integers $a,\\;b,\\;c,\\;d$.
", "showstrings": false, "strings": ["(", "ww", "w*w"], "partialcredit": 0.0}, "checkingaccuracy": 0.001, "vsetrange": [0.0, 1.0], "vsetrangepoints": 5.0, "checkingtype": "absdiff", "answersimplification": "std", "marks": 2.0, "answer": "{a*p}w^3+{a*q+p*b}w^2+{q*b+c*p}w+{c*q}", "type": "jme"}], "steps": [{"prompt": "\nOne way to expand this is as follows:
\n$(pw+q)(aw^2+bw+c)=pw (aw^2+bw+c) +q(aw^2+bw+c)$ etc..
\nOr as $(pw+q)(aw^2+bw+c)=(aw^2+bw+c)(pw+q)$ we can expand it as:
\n$(aw^2+bw+c)(pw+q)=aw^2(pw+q)+bw(pw+q)+c(pw+q)$
\n ", "type": "information", "marks": 0.0}], "marks": 0.0, "type": "gapfill"}], "statement": "Expand the following to give a cubic in $w$.
", "variable_groups": [], "progress": "ready", "type": "question", "variables": {"a": {"definition": "random(1..5)", "name": "a"}, "c": {"definition": "random(2..5)", "name": "c"}, "b": {"definition": "random(-9..9 except [0,a])", "name": "b"}, "d": {"definition": "random(-9..9 except [0,c])", "name": "d"}, "q": {"definition": "random(-3..3 except [0,b,d])", "name": "q"}, "p": {"definition": "random(1..3 except [a,c])", "name": "p"}}, "metadata": {"notes": "\n \t\t \t\t \t\t16/08/2012:
\n \t\t \t\t \t\tAdded tags.
\n \t\t \t\t \t\tAdded description.
\n \t\t \t\t \n \t\t \n \t\t", "description": "Expand $(pw+q)(aw^2+bw+c)$.
", "licence": "Creative Commons Attribution 4.0 International"}, "showQuestionGroupNames": false, "question_groups": [{"name": "", "pickingStrategy": "all-ordered", "pickQuestions": 0, "questions": []}]}, {"name": "Expansion of two brackets: Quadratic and Linear ", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Bill Foster", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/6/"}], "functions": {}, "tags": ["algebra", "algebraic manipulation", "expansion of a quadratic and linear term", "expansion of brackets"], "advice": "\nUsing the method given by Show steps:
\n\\[\\begin{eqnarray*}\\simplify[std]{ ({a}z^2+{b}z+{c})({p}z+{q})}&=&\\simplify[std]{{a}z^2*({p}z+{q})+{b}*z*({p}z+{d})+{c}({p}z+{q})}\\\\&=&\\simplify[std]{{a*p}z^3+{a*q}z^2+{b*p}z^2+{b*d}z+{c*p}z+{c*q}}\\\\&=&\\simplify[std]{{a*p}z^3+{(a*q+b*p)}z^2+{b*d+c*p}z+{c*q}}\\end{eqnarray*}\\]
\n\n ", "rulesets": {"std": ["all", "!noLeadingMinus", "!collectNumbers"]}, "parts": [{"stepspenalty": 1.0, "prompt": "\n
$\\simplify[std]{({a}z^2+{b}z+{c})({p}z+{q})}=\\;$[[0]].
\nYour answer should be a cubic in $z$ and should not include any brackets.
\nYou can click on Show steps for more information, but you will lose one mark if you do so.
\n ", "gaps": [{"notallowed": {"message": "Do not include brackets in your answer. Input your answer as a cubic in $z$, in the form $az^3+bz^2+cz+d$ for appropriate integers $a,\\;b,\\;c,\\;d$.
", "showstrings": false, "strings": ["(", "zz", "z*z"], "partialcredit": 0.0}, "checkingaccuracy": 0.001, "vsetrange": [0.0, 1.0], "vsetrangepoints": 5.0, "checkingtype": "absdiff", "answersimplification": "std", "marks": 2.0, "answer": "{a*p}z^3+{a*q+p*b}z^2+{q*b+c*p}z+{c*q}", "type": "jme"}], "steps": [{"prompt": "\nOne way to expand this is as follows:
\n$(az^2+bz+c)(pz+q)=az^2(pz+q)+bz*(pz+q)+c(pz+q)$ etc..
\n ", "type": "information", "marks": 0.0}], "marks": 0.0, "type": "gapfill"}], "statement": "Expand the following to give a cubic in $z$.
", "variable_groups": [], "progress": "ready", "type": "question", "variables": {"a": {"definition": "random(1..5)", "name": "a"}, "c": {"definition": "random(2..5)", "name": "c"}, "b": {"definition": "random(-9..9 except [0,a])", "name": "b"}, "d": {"definition": "random(-9..9 except [0,c])", "name": "d"}, "q": {"definition": "random(-3..3 except [0,b,d])", "name": "q"}, "p": {"definition": "random(1..3 except [a,c])", "name": "p"}}, "metadata": {"notes": "\n \t\t \t\t16/08/2012:
\n \t\t \t\tAdded tags.
\n \t\t \t\tAdded description.
\n \t\t \n \t\t", "description": "Expand $(az^2+bz+c)(pz+q)$.
", "licence": "Creative Commons Attribution 4.0 International"}, "showQuestionGroupNames": false, "question_groups": [{"name": "", "pickingStrategy": "all-ordered", "pickQuestions": 0, "questions": []}]}, {"name": "Expansion of two brackets: Quadratic and Quadratic ", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Bill Foster", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/6/"}], "functions": {}, "tags": ["algebra", "algebraic manipulation", "expansion of brackets", "expansion of two quadratic terms"], "advice": "\nUsing the method given by Show steps:
\n\\[\\begin{eqnarray*}\\simplify[std]{ ({a}z^2+{b}z+{c})({m}z^2+{p}z+{q})}&=&\\simplify[std]{{a}z^2*({m}z^2+{p}z+{q})+{b}*z*({m}z^2+{p}z+{q})+{c}({m}z^2+{p}z+{q})}\\\\&=&\\simplify[std]{{a*m}z^4+{a*p}z^3+{a*q}z^2+{b*m}z^3+{b*p}z^2+{b*q}z+{c*m}z^2+{c*p}z+{c*q}}\\\\&=&\\simplify[std]{{a*m}z^4+{a*p+m*b}z^3+{(a*q+c*m+b*p)}z^2+{b*q+c*p}z+{c*q}}\\end{eqnarray*}\\]
\n\n ", "rulesets": {"std": ["all", "!noLeadingMinus", "!collectNumbers"]}, "parts": [{"stepspenalty": 1.0, "prompt": "\n
$\\simplify[std]{({a}z^2+{b}z+{c})({m}*z^2+{p}z+{q})}=\\;$[[0]].
\nYour answer should be a quartic (degree 4 polynomial) in $z$ and should not include any brackets.
\nYou can click on Show steps for more information, but you will lose one mark if you do so.
\n ", "gaps": [{"notallowed": {"message": "Do not include brackets in your answer. Input your answer as a quartic in $z$, in the form $az^4+bz^3+cz^2+dz+f$ for appropriate integers $a,\\;b,\\;c,\\;d$ and $f$.
", "showstrings": false, "strings": ["(", "zz", "z*z"], "partialcredit": 0.0}, "checkingaccuracy": 0.001, "vsetrange": [0.0, 1.0], "vsetrangepoints": 5.0, "checkingtype": "absdiff", "answersimplification": "std", "marks": 2.0, "answer": "{a*m}z^4+{a*p+b*m}z^3+{a*q+p*b+c*m}z^2+{q*b+c*p}z+{c*q}", "type": "jme", "maxlength": {"length": 31.0, "message": "Input our answer as a quartic polynomial with all terms cllected together in the form $az^4+bz^3+cz^2+dz+f$ for appropriate integers $a,\\;b,\\;c,\\;d$ and $f$.
", "partialcredit": 0.0}}], "steps": [{"prompt": "\nOne way to expand this is as follows:
\n$(az^2+bz+c)(dz^2+pz+q)=az^2(dz^2+pz+q)+bz(dz^2+pz+q)+c(dz^2+pz+q)$ etc..
\n ", "type": "information", "marks": 0.0}], "marks": 0.0, "type": "gapfill"}], "statement": "Expand the following to give a quartic in $z$.
", "variable_groups": [], "progress": "ready", "type": "question", "variables": {"a": {"definition": "random(1..5)", "name": "a"}, "c": {"definition": "random(2..5)", "name": "c"}, "b": {"definition": "random(-9..9 except [0,a])", "name": "b"}, "d": {"definition": "random(-9..9 except [0,c])", "name": "d"}, "m": {"definition": "random(1..4 except a)", "name": "m"}, "q": {"definition": "random(-3..3 except 0)", "name": "q"}, "p": {"definition": "random(-3..3 except 0)", "name": "p"}}, "metadata": {"notes": "\n \t\t17/08/2012:
\n \t\tAdded tags.
\n \t\tAdded description.
\n \t\tChecked calculation.
\n \t\t", "description": "Expand $(az^2+bz+c)(dz^2+pz+q)$.
", "licence": "Creative Commons Attribution 4.0 International"}, "showQuestionGroupNames": false, "question_groups": [{"name": "", "pickingStrategy": "all-ordered", "pickQuestions": 0, "questions": []}]}, {"name": "Verschil van twee veeltermproducten", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Johan Maertens", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/1301/"}], "advice": "\nExpanding the brackets we have:
\n\\[\\begin{eqnarray*}\\simplify[std]{({a}x+{b})({c}x+{d})-({a}x+{d})({c}x+{b})}&=&(\\simplify[std]{{a*c}x^2+{b*c+a*d}x+{b*d}})-(\\simplify[std]{{a*c}x^2+{b*a+c*d}x+{b*d}})\\\\&=&\\simplify[std]{{b*c+a*d}x-{b*a+c*d}x}\\\\&=&\\var{(a-c)*(d-b)}x\\end{eqnarray*}\\]
\n ", "parts": [{"variableReplacementStrategy": "originalfirst", "marks": 0, "prompt": "$\\simplify[std]{({a}x+{b})({c}x+{d})-({a}x+{d})({c}x+{b})}=\\;$[[0]]
", "scripts": {}, "type": "gapfill", "variableReplacements": [], "gaps": [{"checkingaccuracy": 0.001, "notallowed": {"showStrings": false, "strings": ["("], "message": "Geen haken gebruiken!
", "partialCredit": 0}, "type": "jme", "expectedvariablenames": [], "checkvariablenames": false, "vsetrange": [0, 1], "variableReplacementStrategy": "originalfirst", "showFeedbackIcon": true, "marks": 2, "vsetrangepoints": 5, "showpreview": true, "scripts": {}, "answer": "{(a-c)*(d-b)}*x", "showCorrectAnswer": true, "variableReplacements": [], "maxlength": {"partialCredit": 0, "message": "Je kan de veelterm korter schrijven.
", "length": 6}, "checkingtype": "absdiff", "answersimplification": "std"}], "showFeedbackIcon": true, "showCorrectAnswer": true}], "functions": {}, "variablesTest": {"condition": "", "maxRuns": 100}, "statement": "Werk uit en herleid.
", "rulesets": {"std": ["all", "!collectNumbers", "!noLeadingMinus"]}, "ungrouped_variables": ["c", "a", "d", "b"], "variables": {"c": {"description": "", "definition": "random(-6..6 except [0,a])", "group": "Ungrouped variables", "templateType": "anything", "name": "c"}, "a": {"description": "", "definition": "random(-6..6 except 0)", "group": "Ungrouped variables", "templateType": "anything", "name": "a"}, "d": {"description": "", "definition": "random(1..9 except c)", "group": "Ungrouped variables", "templateType": "anything", "name": "d"}, "b": {"description": "", "definition": "random(1..9 except a)", "group": "Ungrouped variables", "templateType": "anything", "name": "b"}}, "tags": [], "preamble": {"js": "", "css": ""}, "metadata": {"licence": "Creative Commons Attribution 4.0 International", "description": "Simplify $(ax+b)(cx+d)-(ax+d)(cx+b)$. Answer is a multiple of $x$.
"}, "variable_groups": [], "type": "question"}, {"name": "Simplify Algebraic Expressions: 2 unknowns", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Bill Foster", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/6/"}], "functions": {}, "tags": ["algebra", "algebraic manipulation", "expanding brackets", "simplification", "simplifying an expression"], "advice": "\nExpanding the brackets we have:
\n\\[\\begin{eqnarray*}\\simplify[std]{({a}x+{b}y)({c}x+{d}y)-({a}x+{d}y)({c}x+{b}y)}&=&(\\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})\\\\&=&\\simplify[std]{{b*c+a*d}x*y-{b*a+c*d}x*y}\\\\&=&\\var{(a-c)*(d-b)}xy\\end{eqnarray*}\\]
\n ", "rulesets": {"std": ["all", "!collectNumbers", "!noLeadingMinus"]}, "parts": [{"prompt": "\nSimplify:
\n$\\simplify[std]{({a}x+{b}y)({c}x+{d}y)-({a}x+{d}y)({c}x+{b}y)}=\\;$[[0]]
\nDo not include brackets in your answer.
\nInput $xy$ as $x*y$.
\n ", "gaps": [{"notallowed": {"message": "Do not include brackets in your answer.
", "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": "You can simplify the expression further.
", "partialcredit": 0.0}}], "type": "gapfill", "marks": 0.0}], "statement": "Simplify the following expression.
", "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\t18/08/2012:
\n \t\t \t\tAdded tags.
\n \t\t \t\tAdded description.
\n \t\t \n \t\t", "description": "Simplify $(ax+by)(cx+dy)-(ax+dy)(cx+by)$. Answer is a multiple of $xy$.
", "licence": "Creative Commons Attribution 4.0 International"}, "showQuestionGroupNames": false, "question_groups": [{"name": "", "pickingStrategy": "all-ordered", "pickQuestions": 0, "questions": []}]}, {"name": "Johan's copy of Simplify Expression", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Johan Maertens", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/1301/"}], "advice": "\n\\[\\begin{eqnarray*}f(x,y)&=&\\simplify[std]{{a}({b}x+{c}y)+{a1}x+{b1}y+{a2}({b2}x+{c2}y)}\\\\&=&\\simplify[std]{{a*b}x+{a*c}y+{a1}x+{b1}y+{a2*b2}x+{a2*c2}y}\\\\&=&\\simplify[std]{{a*b}x+{a1}x+{a2*b2}x+{a*c}y+{b1}y+{a2*c2}y}\\\\&=&\\simplify[std]{({a*b}+{a1}+{a2*b2})x+({a*c}+{b1}+{a2*c2})y}\\\\&=&\\simplify[std]{{a*b+a1+a2*b2}x+{a*c+b1+a2*c2}y}\\end{eqnarray*}\\]
\n\n ", "rulesets": {"std": ["all", "!collectNumbers", "!noLeadingMinus"]}, "progress": "ready", "question_groups": [{"pickQuestions": 0, "questions": [], "pickingStrategy": "all-ordered", "name": ""}], "statement": "
Express the following expression as $ax+by$ for suitable integers $a$ and $b$.
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", "length": 14.0, "partialcredit": 0.0}}], "prompt": "\nSimplify $f(x,y)=\\simplify[std]{{a}({b}x+{c}y)+{a1}x+{b1}y+{a2}({b2}x+{c2}y)}$
\n$f(x,y)=\\;$[[0]]
\nDo not include brackets in your answer.
\n "}], "functions": {}, "variables": {"f": {"definition": "a*b+a1+a2*b2", "name": "f"}, "c": {"definition": "random(-5..5 except 0)", "name": "c"}, "b": {"definition": "random(1..6)", "name": "b"}, "b1": {"definition": "random(-9..9 except 0)", "name": "b1"}, "a2": {"definition": "random(-5..5 except [0,1,-1])", "name": "a2"}, "d": {"definition": "a*c+b1+a2*c2", "name": "d"}, "a": {"definition": "random(-6..6 except [0,1,-1])", "name": "a"}, "b2": {"definition": "random(-9..9 except [0,a,a1])", "name": "b2"}, "a1": {"definition": "random(-9..9 except [0,a,-a])", "name": "a1"}, "c2": {"definition": "random(-9..9 except 0)", "name": "c2"}}, "metadata": {"licence": "Creative Commons Attribution 4.0 International", "notes": "\n \t\t17/08/2012:
\n \t\tAdded tags.
\n \t\tAdded description.
\n \t\tChecked calculations.OK.
\n \t\t", "description": "Express a sum of linear terms in $x$ and $y$ as a single linear term in $x$ and $y$.
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