Simon's copy of Expansion of two brackets: Linear 2 positive coefficients

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Simon Thomas 6 years ago

Created this as a copy of Expansion of two brackets: Linear 2 positive coefficients.

Name	Status	Author	Last Modified
Expansion of two brackets: Linear 2	draft	Bill Foster	06/08/2020 08:41
Expansion of two brackets: Linear 2 positive coefficients	Ready to use	Julie Crowley	07/10/2016 22:09
Simon's copy of Expansion of two brackets: Linear 2 positive coefficients	draft	Simon Thomas	04/03/2019 09:44
Anna's Expansion of two brackets: Linear 2 positive coefficients - test	draft	Anna Strzelecka	05/07/2019 10:44

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Question statement

Expand the following to give a quadratic in $x$ .

Give any introductory information the student needs.

			Name	Type	Generated Value

a	integer	3
c	integer	2
b	integer	7
d	integer	9

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Description

Describe what this variable represents, and list any assumptions made about its value.

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Generated value: `integer`

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

Your answer should be a quadratic in $x$ and should not include any brackets.

Advice

There are many ways to expand an expression such as $(ax+b)(cx+d)$ .

One method is sometimes referred to as FOIL, a mnemonic to help us remember which terms to multiply with one another:

First $ax \times cx$

Outside $ax \times d$

Inside $b \times cx$

Last $b \times d$

We then add these together and simplify by collecting like terms.

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

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This question is used in the following exam:

Fundamentals of Algebra by Simon Thomas in Maths support.

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Simon's copy of Expansion of two brackets: Linear 2 positive coefficients

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Taxonomy: mathcentre

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Simon Thomas 6 years ago

Error in variable testing condition

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Generated value: `integer`

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Simon's copy of Expansion of two brackets: Linear 2 positive coefficients

Metadata

Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

Contributors

History

Comment

Checkpoint description

Simon Thomas 6 years ago

Error in variable testing condition

Error

Warning

Generated value: integer

Parts

Gap-fill

Generated value: `integer`