1.3.1. Addition and Subtraction of Like Terms

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Name	Status	Author	Last Modified
1.3.1. Addition and Subtraction of Like Terms	Ready to use	Merryn Horrocks	28/06/2023 05:42
1.3.1. Task: Collect like terms 1	Ready to use	Merryn Horrocks	15/07/2023 01:53
1.3.1. Task: Collect like terms 2	Ready to use	Merryn Horrocks	15/07/2023 01:53

Question statement

Addition and Subtraction of Like Terms

Like terms are multiples of the same quantity. For example $5y$ , $17y$ and $\displaystyle{\frac{1}{2}y}$ are all multiples of $y$ and so are like terms. Similarly, $3x^2$ , $-5x^2$ and $\displaystyle{\frac{1}{4}x^2}$ are all multiples of $x^2$ and so are like terms.

Further examples of like terms are:

$kx$ and $mx$ which are both multiples of $x$ ,

$x^2y$ , $6x^2y$ , $-13x^2y$ , $-2yx^2$ , which are all multiples of $x^2y$ ,

$abc^2$ , $-7abc^2$ , $kabc^2$ , which are multiples of $abc^2$

Like terms can be added or subtracted in order to simplify expressions.

Example 27

Simplify $5x-13x+22x$

Solution

All three terms are multiples of $x$ and so are like terms. The expression can be simplified to $14x$ .

Example 28

Simplify $5z+2x$

Solution

$5z$ and $2x$ are not like terms. They are not multiples of the same quantity. This expression cannot be simplified.

Give any introductory information the student needs.

			Name	Type	Generated Value

q1letter1	string	m
q1letter2	string	x
q1ints	list	[ -17, -17, -16, -7 ]
q1expr	expression	-17m - 17x - 16m - 7x
q1ans	expression	-33m - 24x

			Name	Type	Generated Value

q2letter1	string	g
q2letter2	string	f
q2coeffs	list	[ -1/3, -3, -3/4 ]
q2expr	expression	-(1/3)g - 3g - (3/4)f
q2ans	expression	-(10/3)g - (3/4)f

			Name	Type	Generated Value

alphabet

list

List of 21 items

Automatically regenerate variables?

Name

Data type

Value

xxxxxxxxxx
 
random(alphabet)

JME function reference

Description

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

Can an exam override the value of this variable?

Generated value: `string`

← Depends on:

This variable doesn't seem to be used anywhere.

Advice

By collecting like terms, $\var{q1expr} = \var{q1ans}$

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This question is used in the following exam:

HELM Book 1.3 Simplification and Factorisation by Merryn Horrocks in HELM books.

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1.3.1. Addition and Subtraction of Like Terms

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Merryn Horrocks 1 year, 10 months ago

Merryn Horrocks 2 years, 10 months ago

Merryn Horrocks 2 years, 11 months ago

Addition and Subtraction of Like Terms

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Generated value: `string`

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1.3.1. Addition and Subtraction of Like Terms

Metadata

Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

Contributors

Feedback

History

Comment

Checkpoint description

Merryn Horrocks 1 year, 10 months ago

Merryn Horrocks 2 years, 10 months ago

Merryn Horrocks 2 years, 11 months ago

Addition and Subtraction of Like Terms

Error in variable testing condition

Error

Warning

Generated value: string

Parts

Mathematical expression

Advanced settings

Checking accuracy

Variable value generators

Pattern restriction

Variables

String restrictions

Generated value: `string`