Simplify Expression

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Bill Foster

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Bill Foster 55 years, 2 months ago

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Question statement

Express the following expression as $ax+by$ for suitable integers $a$ and $b$ .

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			Name	Type	Generated Value

a	integer	-5
c	integer	-2
b	integer	2
d	integer	-13
f	integer	21
a1	integer	3
a2	integer	-4
b1	integer	5
b2	integer	-7
c2	integer	7

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Value

xxxxxxxxxx
 
random(-6..6 except [0,1,-1])

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Generated value: `integer`

-5

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Gap-fill
1. Gap Mathematical expression
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Gap-fill

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Simplify $f(x,y)=\simplify[std]{{a}({b}x+{c}y)+{a1}x+{b1}y+{a2}({b2}x+{c2}y)}$

$f(x,y)=\;$ Unnamed gap

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Advice

$\begin{eqnarray*}f(x,y)&=&\simplify[std]{{a}({b}x+{c}y)+{a1}x+{b1}y+{a2}({b2}x+{c2}y)}\\&=&\simplify[std]{{a*b}x+{a*c}y+{a1}x+{b1}y+{a2*b2}x+{a2*c2}y}\\&=&\simplify[std]{{a*b}x+{a1}x+{a2*b2}x+{a*c}y+{b1}y+{a2*c2}y}\\&=&\simplify[std]{({a*b}+{a1}+{a2*b2})x+({a*c}+{b1}+{a2*c2})y}\\&=&\simplify[std]{{a*b+a1+a2*b2}x+{a*c+b1+a2*c2}y}\end{eqnarray*}$

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This question is used in the following exams:

Week 2 Qs by Peter Chapman in Peter's workspace.
Basic Algebraic Manipulation: Expansion of Brackets by Bill Foster in Bill's workspace.
mathcentre: Expanding brackets by Bill Foster in Bill's workspace.
Maths Support: Expanding brackets by Christian Lawson-Perfect in Maths Support Wiki.
Expanding Brackets by Jessica Ryan in Jessica's workspace.
Algebraic manipulation: 1 by Aneela Arshad in Aneela's workspace.
Expanding Brackets by Gareth Woods in Gareth's workspace.
Drieterm vermenigvuldigen met drieterm by Johan Maertens in Johan's workspace.
productos de polinomios by Guillermo Bernardo DURÁN GONZÁLEZ in Numbas N° 7.
Practice Math by Isabel Cooke in Isabel's workspace.
Don's copy of Maths Support: Expanding brackets by Don Shearman in Don's workspace.

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Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

Contributors

History

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Checkpoint description

Bill Foster 55 years, 2 months ago

Error in variable testing condition

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Generated value: `integer`

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Gap-fill

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Simplify Expression

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`