random variables for part 1
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$\\var{a[1]}x^2+\\var{a[2]}x^2+\\var{a[3]}x+\\var{a[4]}x +\\var{a[0]}=$ [[0]]
You must condense your answer to fully simplify.
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You must condense your answer to fully simplify.
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", "unitTests": [], "customName": ""}, {"extendBaseMarkingAlgorithm": true, "showCorrectAnswer": true, "useCustomName": false, "showFeedbackIcon": true, "gaps": [{"showCorrectAnswer": true, "checkVariableNames": false, "useCustomName": false, "mustmatchpattern": {"nameToCompare": "", "partialCredit": 0, "pattern": "$n*x+$n*y", "message": "You haven't simplified: you still have two or more like terms that should be collected together."}, "unitTests": [], "answerSimplification": "all", "showFeedbackIcon": true, "type": "jme", "variableReplacementStrategy": "originalfirst", "failureRate": 1, "variableReplacements": [], "vsetRange": [0, 1], "maxlength": {"partialCredit": 0, "message": "You must condense your answer to fully simplify. *'s are not needed to indicate multiplication here.
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\n", "unitTests": [], "customName": ""}, {"extendBaseMarkingAlgorithm": true, "showCorrectAnswer": true, "useCustomName": false, "showFeedbackIcon": true, "gaps": [{"showCorrectAnswer": true, "checkVariableNames": true, "useCustomName": false, "mustmatchpattern": {"nameToCompare": "", "partialCredit": 0, "pattern": "$n*x*z + $n*x^2 + $n*x + $n*z + $n*z^2", "message": "You haven't simplified: you still have two or more like terms that should be collected together."}, "unitTests": [], "answerSimplification": "all", "showFeedbackIcon": true, "type": "jme", "musthave": {"partialCredit": 0, "message": "", "strings": ["*"], "showStrings": false}, "variableReplacementStrategy": "originalfirst", "failureRate": 1, "notallowed": {"partialCredit": 0, "message": "9You should not have brackets in your answer.
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", "length": "0"}, "customMarkingAlgorithm": "", "vsetRangePoints": 5, "valuegenerators": [{"value": "", "name": "x"}, {"value": "", "name": "z"}], "customName": "", "extendBaseMarkingAlgorithm": true, "checkingAccuracy": 0.001, "answer": "({h[0]}{h[1]}+{h[4]})x^2+({h[0]}{h[2]})z*x+{h[3]}x+{h[5]}z^2+{h[6]}z", "checkingType": "absdiff", "scripts": {}, "showPreview": true, "marks": 1}], "type": "gapfill", "variableReplacementStrategy": "originalfirst", "sortAnswers": false, "scripts": {}, "customMarkingAlgorithm": "", "marks": 0, "variableReplacements": [], "prompt": "$\\var{h[0]}x(\\var{h[1]}x+\\var{h[2]}z)+\\var{h[3]}x+\\var{h[6]}z+\\var{h[4]}x^2+\\var{h[5]}z^2=$ [[0]]
", "unitTests": [], "customName": ""}, {"extendBaseMarkingAlgorithm": true, "showCorrectAnswer": true, "useCustomName": false, "showFeedbackIcon": true, "gaps": [{"showCorrectAnswer": true, "checkVariableNames": true, "useCustomName": false, "mustmatchpattern": {"nameToCompare": "", "partialCredit": 0, "pattern": "$n*x + `+-$n*y", "message": "You haven't simplified: you still have two or more like terms that should be collected together."}, "unitTests": [], "answerSimplification": "all", "showFeedbackIcon": true, "type": "jme", "variableReplacementStrategy": "originalfirst", "failureRate": 1, "variableReplacements": [], "vsetRange": [0, 1], "maxlength": {"partialCredit": 0, "message": "You must condense your answer to fully simplify.
", "length": "0"}, "customMarkingAlgorithm": "", "vsetRangePoints": 5, "valuegenerators": [{"value": "", "name": "x"}, {"value": "", "name": "y"}], "customName": "", "extendBaseMarkingAlgorithm": true, "checkingAccuracy": 0.001, "answer": "({j[0]}{j[1]}+{j[4]}{j[3]}+{j[6]}{j[7]})x-({j[0]}{j[2]}+{j[5]}{j[3]}+{j[6]}{j[8]})y", "checkingType": "absdiff", "scripts": {}, "showPreview": true, "marks": 1}], "type": "gapfill", "variableReplacementStrategy": "originalfirst", "sortAnswers": false, "scripts": {}, "customMarkingAlgorithm": "", "marks": 0, "variableReplacements": [], "prompt": "$\\var{j[0]}(\\var{j[1]}x-\\var{j[2]}y)+\\var{j[3]}(\\var{j[4]}x-\\var{j[5]}y)+\\var{j[6]}(\\var{j[7]}x-\\var{j[8]}y)=$ [[0]]
", "unitTests": [], "customName": ""}], "advice": "When simplifying expressions, only terms of the same type or like terms can be added together.
\nAlgebraic symbols or letters can be added together provided that they are raised to the same power. For example, we can add $x^2+x^2=2x^2$, but we cannot collect both $x^2$ and $x$ into one term.
\n\\[
\\begin{align}
\\var{c[0]}x+\\var{c[1]}x+\\var{c[2]}x&=(\\var{c[0]}+\\var{c[1]}+\\var{c[2]})x\\\\
&=\\simplify{({c[0]}+{c[1]}+{c[2]})}x
\\end{align}
\\]
\\[
\\begin{align}
\\var{a[1]}x^2+\\var{a[2]}x^2+\\var{a[3]}x+\\var{a[4]}x +\\var{a[0]}&=(\\var{a[1]}+\\var{a[2]})x^2+(\\var{a[3]}+\\var{a[4]})x +\\var{a[0]}\\\\
&=\\simplify{({a[1]}+{a[2]})}x^2+\\simplify{({a[3]}+{a[4]})}x+\\var{a[0]}
\\end{align}
\\]
\\[
\\begin{align}
\\var{b[0]}y^5+\\var{b[1]}y^5+\\var{b[2]}y^5+\\var{b[4]}y^5+\\var{b[3]}y^5&=(\\var{b[0]}+\\var{b[1]}+\\var{b[2]}+\\var{b[4]}+\\var{b[3]})y^5\\\\
&=\\simplify{({b[1]}+{b[2]}+{b[3]}+{b[4]}+{b[0]})}y^5
\\end{align}
\\]
\\[
\\begin{align}
\\var{d[0]}ab+\\var{d[1]}abc+\\var{d[2]}a+\\var{d[3]}b+\\var{d[4]}c+\\var{d[5]}abc
&=(\\var{d[1]}+\\var{d[5]})abc+\\var{d[0]}ab+\\var{d[2]}a+\\var{d[3]}b+\\var{d[4]}c\\\\
&=\\simplify{{d[1]}+{d[5]}}abc+\\var{d[0]}ab+\\var{d[2]}a+\\var{d[3]}b+\\var{d[4]}c
\\end{align}
\\]
\\[
\\begin{align}
\\var{f[0]}a^2b+\\var{f[1]}ab^2+\\var{f[2]}ab+\\var{f[3]}a^2b+\\var{f[4]}ab^2
&=(\\var{f[0]}+\\var{f[3]})a^2b+(\\var{f[1]}+\\var{f[4]})ab^2+\\var{f[2]}ab\\\\
&=\\simplify{{f[0]}+{f[3]}}a^2b+\\simplify{{f[1]}+{f[4]}}ab^2+\\var{f[2]}ab
\\end{align}
\\]
\\[
\\begin{align}
\\var{g[0]}(\\var{g[1]}x+\\var{g[2]}y)+\\var{g[4]}x+\\var{g[5]}y
&=(\\var{g[0]}\\times \\var{g[1]}+\\var{g[4]})x+(\\var{g[0]} \\times\\var{g[2]}+\\var{g[5]})y\\\\
&=(\\simplify{{g[0]}*{g[1]}}+\\var{g[4]})x+(\\simplify{{g[0]}*{g[2]}}+\\var{g[5]})y\\\\
&=\\simplify{{g[0]}*{g[1]}+{g[4]}}x+\\simplify{{g[0]}*{g[2]}+{g[5]}}y
\\end{align}
\\]
\\[
\\begin{align}
\\var{h[0]}x(\\var{h[1]}x+\\var{h[2]}z)+\\var{h[3]}x+\\var{h[6]}z+\\var{h[4]}x^2+\\var{h[5]}z^2
&=(\\simplify[]{{h[0]}{h[1]}}+\\var{h[4]})x^2+(\\simplify[]{{h[0]}{h[2]}})zx+\\var{h[3]}x+\\var{h[5]}z^2+\\var{h[6]}z\\\\
&=(\\simplify{{h[0]}{h[1]}}+\\var{h[4]})x^2+(\\simplify[]{{h[0]}{h[2]}})zx+\\var{h[3]}x+\\var{h[5]}z^2+\\var{h[6]}z\\\\
&=\\simplify{{h[0]}*{h[1]}+{h[4]}}x^2+\\simplify{{h[0]}*{h[2]}}zx+\\simplify{{h[3]}x+{h[5]}}z^2+\\var{h[6]}z
\\end{align}
\\]
\\[
\\begin{align}
\\var{j[0]}(\\var{j[1]}x-\\var{j[2]}y)+\\var{j[3]}(\\var{j[4]}x-\\var{j[5]}y)+\\var{j[6]}(\\var{j[7]}x-\\var{j[8]}y)
&= (\\simplify[]{{j[0]}{j[1]}}+\\simplify[]{{j[3]}{j[4]}}+\\simplify[]{{j[6]}{j[7]}})x-(\\simplify[]{{j[0]}{j[2]}}+\\simplify[]{{j[3]}{j[5]}}+\\simplify[]{{j[6]}{j[8]}})y\\\\
&= (\\simplify{{j[0]}{j[1]}}+\\simplify{{j[3]}{j[4]}}+\\simplify{{j[6]}{j[7]}})x-(\\simplify{{j[0]}{j[2]}}+\\simplify{{j[3]}{j[5]}}+\\simplify{{j[6]}{j[8]}})y\\\\
&= \\simplify{({j[0]}*{j[1]}+{j[4]*j[3]}+{j[6]}*{j[7]})x}-\\simplify{({j[0]}*{j[2]}+{j[5]}{j[3]}+{j[6]}*{j[8]})y}
\\end{align}
\\]
For each expression below, collect like terms and expand brackets.
\nThe * symbol is required between algebraic symbols, e.g. $5ab^2$ should be written 5*a*b^2.
Eight expressions, of increasing complexity. The student must simplify them by expanding brackets and collecting like terms.
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