Expansion of three brackets: (Video)

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Bill Foster

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Bill Foster 55 years, 2 months ago

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Question statement

Expand the following to give a cubic in $y$ .

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			Name	Type	Generated Value

a	integer	4
c	integer	4
b	integer	6
d	integer	-1
q	integer	1
p	integer	3

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Generated value: `integer`

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1. Gap Mathematical expression
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Gap-fill

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$\simplify[std]{({a}y+{b})({c}y+{d})({p}y+{q})}=\;$ Unnamed gap.

Your answer should be a cubic in $y$ and should not include any brackets.

You can click on Show steps for more information, but you will lose one mark if you do so.

There is a video in Show steps which expands three brackets, but uses the variable $x$ rather than $y$ .

Advice

Using the method given by Show steps we first multiply out the first two brackets:

$\begin{eqnarray*}\simplify[std]{ ({a}y+{b})({c}y+{d})}&=&\simplify[std]{{a}y*({c}y+{d})+{b}({c}y+{d})}\\&=&\simplify[std]{{a*c}y^2+{a*d}y+{b*c}y+{b*d}}\\&=&\simplify[std]{{a*c}y^2+{(a*d+b*c)}y+{b*d}}\end{eqnarray*}$

And then multiply this by the third bracket:

$\begin{eqnarray*}\simplify[std]{({a}y+{b})({c}y+{d})({p}y+{q})}&=&\simplify[std]{({a*c}y^2+{(a*d+b*c)}y+{b*d})({p}y+{q})}\\&=&\simplify[std]{{a*c}y^2({p}y+{q})+{(a*d+b*c)}y*({p}y+{q})+{b*d}({p}y+{q})}\\&=&\simplify[std]{{a*c*p}*y^3 +{a*c*q}*y^2+{p*(a*d+b*c)}y^2+{q*(a*d+b*c)}y+{b*d*p}y+{b*d*q}}\\&=&\simplify[std]{{a*c*p}y^3+{a*c*q+a*d*p+p*b*c}y^2+{a*d*q+b*c*q+b*d*p}y+{b*d*q}}\end{eqnarray*}$

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Taxonomy: mathcentre

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Taxonomy: Context

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Bill Foster 55 years, 2 months ago

Error in variable testing condition

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Generated value: `integer`

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Expansion of three brackets: (Video)

Metadata

Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

Contributors

History

Comment

Checkpoint description

Bill Foster 55 years, 2 months ago

Error in variable testing condition

Error

Warning

Generated value: integer

Parts

Gap-fill

Generated value: `integer`