<?xml version="1.0" encoding="UTF-8"?>
<quiz>
  <question type="stack">
    <name>
      <text>1.3.3.2 Removing 2 sets of brackets</text>
    </name>
    <questiontext format="html">
      <text><![CDATA[<p class="HELM_exercise">Exercise</p>
<p>Remove the brackets from each of the following expressions:<br></p>

<ol class="HELM_parts">

<li><p>\( ({@a1@}+a)({@a2@}+b)=\) [[input:ans1]] [[validation:ans1]] [[feedback:prt1]]</p></li>

<li><p>\( (x + {@b1@})(x + {@b2@})=\) [[input:ans2]] [[validation:ans2]] [[feedback:prt2]]</p></li>

<li><p> \((x + {@c1@})(x + {@c2@})=\) [[input:ans3]] [[validation:ans3]] [[feedback:prt3]]</p></li>

<li><p> \((x + {@d1@})(x - {@d2@})=\) [[input:ans4]] [[validation:ans4]] [[feedback:prt4]]</p></li>

</ol>]]></text>
    </questiontext>
    <generalfeedback format="html">
      <text><![CDATA[<ol class="HELM_parts">
    <li>
        <p>\[ ({@a1@}+a) ({@a2@}+b) =({@a1@}+a) ({@a2@}) + ({@a1@}+a)(b) \]</p>
        <p>\[ = ({@a1@})({@a2@}) + (a)({@a2@}) + ({@a1@})(b) + (a)(b) \]</p>
        <p>\[ = {@a1*a2@} + {@a2@}a + {@a1@}b + ab. \]</p>
    </li>
          
    <li>
<p>\[ (x + {@b1@}) (x + {@b2@})= (x + {@b1@}) (x) + (x + {@b1@})({@b2@}) \]</p>
        <p>\[ = (x)(x) + ({@b1@})(x) + ({@b2@})(x) + ({@b1@})({@b2@}) \]</p>
        <p>\[ = x^2 + {@b1 + b2@}x + {@b1*b2@}. \]</p>
    </li>
  
    <li>
        <p>\[ (x + {@c1@}) (x + {@c2@})= (x + {@c1@}) (x) + (x + {@c1@})({@c2@}) \]</p>
        <p>\[ = (x)(x) + ({@c1@})(x) + ({@c2@})(x) + ({@c1@})({@c2@}) \]</p>
        <p>\[ = x^2 + {@c1 + c2@}x + {@c1*c2@}. \]</p>
    </li>
  
    <li>
        <p>\[ (x + {@d1@}) (x - {@d2@})= (x + {@d1@}) (x) - (x + {@d1@})({@d2@}) \]</p>
        <p>\[ = (x)(x) + ({@d1@})(x) - ({@d2@})(x) - ({@d1@})({@d2@}) \]</p>
        <p>\[ = x^2 + {@d1 - d2@}x - {@d1*d2@}. \]</p>
    </li>
</ol>]]></text>
    </generalfeedback>
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    <idnumber/>
    <stackversion>
      <text>2021072200</text>
    </stackversion>
    <questionvariables>
      <text>a1: rand(2)+3;
a2:a1+1;
ta1: a1*a2 + b*a1 + a*a2 + a*b;

b1: rand(2)+2;
b2:b1+1;
ta2: x^2 + (b1+b2)*x + b1*b2;
ta2f: x^2 + (b1*x) + b2*x + b1*b2;

c1: rand(3)+3;
c2:c1;
ta3: x^2 + (c1+c2)*x + c1*c2;
ta3f:x^2 + c1*x + c2*x + c1*c2;

d1: rand(2)+6;
d2:d1-2;
ta4: x^2 + (d1 - d2)*x - d1*d2;
ta4f:x^2 + d1*x -d2*x -d1*d2;</text>
    </questionvariables>
    <specificfeedback format="html">
      <text/>
    </specificfeedback>
    <questionnote format="moodle_auto_format">
      <text>\({@ta1@}, \, {@ta2@}, \, {@ta3@}, \,  {@ta4@}\)</text>
    </questionnote>
    <questiondescription format="moodle_auto_format">
      <text/>
    </questiondescription>
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      <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Correct answer, well done.]]></text>
    </prtcorrect>
    <prtpartiallycorrect format="html">
      <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Your answer is partially correct.]]></text>
    </prtpartiallycorrect>
    <prtincorrect format="html">
      <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Incorrect answer.]]></text>
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    <decimals>.</decimals>
    <scientificnotation>*10</scientificnotation>
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      <name>ans4</name>
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      <tans>ta4</tans>
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          <text><![CDATA[<p>\[ ({@a1@}+a) ({@a2@}+b) =&nbsp;({@a1@}+a) ({@a2@}) + ({@a1@}+a)(b) \]</p>
<p>\[ = ({@a1@})({@a2@}) + (a)({@a2@}) + ({@a1@})(b) + (a)(b) \]</p>
<p>\[ = {@a1*a2@} + {@a2@}a + {@a1@}b + ab. \]&nbsp;</p>]]></text>
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      <node>
        <name>1</name>
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        <answertest>AlgEquiv</answertest>
        <sans>ans2</sans>
        <tans>ta2</tans>
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        <truefeedback format="html">
          <text><![CDATA[<p>You have removed the brackets correctly, but you have not simplified your answer fully.</p><p></p><p>\[ (x + {@b1@}) (x + {@b2@})= (x + {@b1@}) (x) +&nbsp;(x + {@b1@})&nbsp;({@b2@}) \]</p><p>\[ = (x)(x) + ({@b1@})(x) + ({@b2@})(x) + ({@b1@})({@b2@}) \]</p><p>\[ = x^2 + {@b1 + b2@}x + {@b1*b2@}. \]&nbsp;</p><br><br><p></p>]]></text>
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        <falsefeedback format="html">
          <text><![CDATA[<p></p><p>\[ (x + {@b1@}) (x + {@b2@})= (x + {@b1@}) (x) +&nbsp;(x + {@b1@})&nbsp;({@b2@}) \]</p><p>\[ = (x)(x) + ({@b1@})(x) + ({@b2@})(x) + ({@b1@})({@b2@}) \]</p><p>\[ = x^2 + {@b1 + b2@}x + {@b1*b2@}. \]&nbsp;</p><br><p></p>]]></text>
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        <name>1</name>
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          <text><![CDATA[<p></p><p>You have removed the brackets correctly, but you have not simplified your answer fully.<br></p><p></p><p>\[ (x + {@c1@}) (x + {@c2@})= (x + {@c1@}) (x) + (x + {@c1@})({@c2@}) \]</p><p>\[ = (x)(x) + ({@c1@})(x) + ({@c2@})(x) + ({@c1@})({@c2@}) \]</p><p>\[ = x^2 + {@c1 + c2@}x + {@c1*c2@}. \]</p><p></p><br><p></p>]]></text>
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          <text><![CDATA[<p>\[ (x + {@c1@}) (x + {@c2@})= (x + {@c1@}) (x) + (x + {@c1@})({@c2@}) \]<br></p><p></p><p>\[ = (x)(x) + ({@c1@})(x) + ({@c2@})(x) + ({@c1@})({@c2@}) \]</p><p>\[ = x^2 + {@c1 + c2@}x + {@c1*c2@}. \]</p><br><br><p></p>]]></text>
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        <answertest>AlgEquiv</answertest>
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        <truefeedback format="html">
          <text><![CDATA[<p></p><p>You have removed the brackets correctly, but you have not simplified your answer fully.<br></p><p></p><p>\[ (x + {@d1@}) (x - {@d2@})= (x + {@d1@}) (x) - (x + {@d1@})({@d2@}) \]</p><p>\[ = (x)(x) + ({@d1@})(x) - ({@d2@})(x) - ({@d1@})({@d2@}) \]</p><p>\[ = x^2 + {@d1 - d2@}x - {@d1*d2@}. \]</p><br><p></p><p></p><p><br></p><br><br><p></p>]]></text>
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          <text><![CDATA[<p></p><p>\[ (x + {@d1@}) (x - {@d2@})= (x + {@d1@}) (x) - (x + {@d1@})({@d2@}) \]</p><p>\[ = (x)(x) + ({@d1@})(x) - ({@d2@})(x) - ({@d1@})({@d2@}) \]</p><p>\[ = x^2 + {@d1 - d2@}x - {@d1*d2@}. \]</p><br><p></p>]]></text>
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        <value>ta2</value>
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      <testinput>
        <name>ans3</name>
        <value>ta3</value>
      </testinput>
      <testinput>
        <name>ans4</name>
        <value>ta4</value>
      </testinput>
      <expected>
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        <expectedscore>1.0000000</expectedscore>
        <expectedpenalty>0.0000000</expectedpenalty>
        <expectedanswernote>prt1-1-T</expectedanswernote>
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        <expectedpenalty>0.0000000</expectedpenalty>
        <expectedanswernote>prt2-1-T</expectedanswernote>
      </expected>
      <expected>
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        <expectedscore>1.0000000</expectedscore>
        <expectedpenalty>0.0000000</expectedpenalty>
        <expectedanswernote>prt3-1-T</expectedanswernote>
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        <name>ans1</name>
        <value>ta2</value>
      </testinput>
      <testinput>
        <name>ans2</name>
        <value>ta3</value>
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      <testinput>
        <name>ans3</name>
        <value>ta4</value>
      </testinput>
      <testinput>
        <name>ans4</name>
        <value>ta1</value>
      </testinput>
      <expected>
        <name>prt1</name>
        <expectedscore>0.0000000</expectedscore>
        <expectedpenalty>0.1000000</expectedpenalty>
        <expectedanswernote>prt1-1-F</expectedanswernote>
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      <expected>
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        <expectedscore>0.0000000</expectedscore>
        <expectedpenalty>0.1000000</expectedpenalty>
        <expectedanswernote>prt2-2-F</expectedanswernote>
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      <expected>
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        <expectedscore>0.0000000</expectedscore>
        <expectedpenalty>0.1000000</expectedpenalty>
        <expectedanswernote>prt3-2-F</expectedanswernote>
      </expected>
      <expected>
        <name>prt4</name>
        <expectedscore>0.0000000</expectedscore>
        <expectedpenalty>0.1000000</expectedpenalty>
        <expectedanswernote>prt4-2-F</expectedanswernote>
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    <qtest>
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      <testinput>
        <name>ans1</name>
        <value>ta1</value>
      </testinput>
      <testinput>
        <name>ans2</name>
        <value> x^2 + (b1*x) + b2*x + b1*b2</value>
      </testinput>
      <testinput>
        <name>ans3</name>
        <value>x^2 + c1*x + c2*x + c1*c2</value>
      </testinput>
      <testinput>
        <name>ans4</name>
        <value>x^2 + d1*x -d2*x -d1*d2</value>
      </testinput>
      <expected>
        <name>prt1</name>
        <expectedscore>1.0000000</expectedscore>
        <expectedpenalty>0.0000000</expectedpenalty>
        <expectedanswernote>prt1-1-T</expectedanswernote>
      </expected>
      <expected>
        <name>prt2</name>
        <expectedscore>0.5000000</expectedscore>
        <expectedpenalty>0.1000000</expectedpenalty>
        <expectedanswernote>prt2-2-T</expectedanswernote>
      </expected>
      <expected>
        <name>prt3</name>
        <expectedscore>0.5000000</expectedscore>
        <expectedpenalty>0.1000000</expectedpenalty>
        <expectedanswernote>prt3-2-T</expectedanswernote>
      </expected>
      <expected>
        <name>prt4</name>
        <expectedscore>0.5000000</expectedscore>
        <expectedpenalty>0.1000000</expectedpenalty>
        <expectedanswernote>prt4-2-T</expectedanswernote>
      </expected>
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  </question>
</quiz>
