Pre-Calc/Chapter 9: Discrete Mathematics/9.2 The Binomial Theorem/9.2.1 Expand Binomial Expression
Expand the Binomial
«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo»(«/mo»«mn»3«/mn»«mi»x«/mi»«mo»+«/mo»«mn»5«/mn»«msup»«mo»)«/mo»«mn»3«/mn»«/msup»«mo»=«/mo»«/math»]]>
1.0000000
0.3333333
0
true
true
abc
«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mn»9«/mn»«msup»«mi»x«/mi»«mn»2«/mn»«/msup»«mo»+«/mo»«mn»30«/mn»«mi»x«/mi»«mo»+«/mo»«mn»25«/mn»«/math»]]>
«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mn»27«/mn»«msup»«mi»x«/mi»«mn»3«/mn»«/msup»«mo»+«/mo»«mn»135«/mn»«msup»«mi»x«/mi»«mn»2«/mn»«/msup»«mo»+«/mo»«mn»225«/mn»«mi»x«/mi»«mo»+«/mo»«mn»125«/mn»«/math»]]>
«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mn»27«/mn»«msup»«mi»x«/mi»«mn»3«/mn»«/msup»«mo»+«/mo»«mn»135«/mn»«msup»«mi»x«/mi»«mn»2«/mn»«/msup»«mo»+«/mo»«mn»135«/mn»«mi»x«/mi»«mo»+«/mo»«mn»125«/mn»«/math»]]>
«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mn»9«/mn»«msup»«mi»x«/mi»«mn»6«/mn»«/msup»«mo»+«/mo»«mn»15«/mn»«msup»«mi»x«/mi»«mn»3«/mn»«/msup»«mo»+«/mo»«mn»15625«/mn»«/math»]]>
<question><correctAnswers><correctAnswer></correctAnswer></correctAnswers></question>
Pre-Calc/Chapter 9: Discrete Mathematics/9.2 The Binomial Theorem/9.2.2 Evaluate a Binomial Coefficient
Evaluating Combinations
Evaluate combinations of #n objects chosen #r at a time.]]>
1.0000000
0.3333333
0
0
#answer]]>
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Pre-Calc/Chapter 9: Discrete Mathematics/9.2 The Binomial Theorem/9.2.3 Find Coefficient of Given Term in Expansion
Find coefficient of a given term
Find the coefficient of the «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«msup»«mi»x«/mi»«mrow»«mo»#«/mo»«mi»a«/mi»«/mrow»«/msup»«msup»«mi»y«/mi»«mrow»«mo»#«/mo»«mi»b«/mi»«/mrow»«/msup»«/math» term in the expansion of «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo»(«/mo»«mi»x«/mi»«mo»+«/mo»«mi»y«/mi»«msup»«mo»)«/mo»«mrow»«mo»#«/mo»«mi»n«/mi»«/mrow»«/msup»«/math»]]>
1.0000000
0.3333333
0
0
#answer]]>
<question><wirisCasSession><![CDATA[<session lang="en" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="en">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>6</mn><mo>.</mo><mo>.</mo><mn>12</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>2</mn><mo>.</mo><mo>.</mo><mn>7</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi><mo>=</mo><mi>n</mi><mo>-</mo><mi>a</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>answer</mi><mo>=</mo><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">C</csymbol><mi>n</mi><mi>a</mi></apply></math></input></command></group></library></session>]]></wirisCasSession><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><mo>#</mo><mi>a</mi><mi>n</mi><mi>s</mi><mi>w</mi><mi mathvariant="normal">e</mi><mi>r</mi></math>]]></correctAnswer><correctAnswer id="1"></correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-4)</option><option name="relative_tolerance">false</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="cas">add</data><data name="inputField">inlineEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession">null</data></localData></question>