1.3.2. Removing Brackets from a(b+c) and a(b-c)

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Name	Status	Author	Last Modified
1.3.2. Removing Brackets from a(b+c) and a(b-c)	Ready to use	Merryn Horrocks	28/06/2023 05:45
1.3.2. Task: Remove brackets 1	Ready to use	Merryn Horrocks	20/07/2023 02:56
1.3.2. Task: Remove brackets 2	Ready to use	Merryn Horrocks	20/07/2023 03:05
1.3.2. Task: Remove brackets 3	Ready to use	Merryn Horrocks	20/07/2023 03:05
1.3.2. Task: Remove brackets 4	Ready to use	Merryn Horrocks	20/07/2023 03:05
1.3.2. Task: Remove brackets 5	Ready to use	Merryn Horrocks	20/07/2023 03:03

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Question statement

Removing Brackets from expressions $a(b+c)$ and $a(b-c)$

Removing brackets means multiplying out. For example

$5(2+4) = 5\times 2+5\times 4 = 10+20 = 30.$

In this simple example we could alternatively get the same result as follows:

$5(2 + 4) = 5 \times 6 = 30.$

That is:

$5(2 + 4) = 5 \times 2 + 5 \times 4$

In an expression such as $5(x+y)$ it is intended that the $5$ multiplies both $x$ and $y$ to produce $5x+5y$ .

Thus the expressions $5(x + y)$ and $5x + 5y$ are equivalent. In general we have the following rules known as distributive laws:

Key Point 14

$a(b+c)=ab+ac$

$a(b-c)=ab-ac$

Note that when the brackets are removed both terms in the brackets are multiplied by $a$ .

As we have noted above, if you insert numbers instead of letters into these expressions you will see that both left and right hand sides are equivalent. For example

$4(3 + 5)$ has the same value as $4(3) + 4(5)$ ; that is $32$

and

$7(8 - 3)$ has the same value as $7(8) - 7(3)$ ; that is $35$

Example 31

Remove the brackets from (a) $9(2+y),\quad$ (b) $9(2y)$

Solution

(a) In the expression $9(2 + y)$ the $9$ must multiply both terms in the brackets:

$\begin{align*} 9(2+y)&=9(2)+9(y) \\ &=18+9y \end{align*}$

(b) Recall that $9(2y)$ means $9 \times (2 \times y)$ and that when multiplying numbers together the presence of brackets is irrelevant. Thus $9(2y) = 9 \times 2 \times y = 18y$

The crucial distinction between the role of the factor $9$ in the two expressions $9(2 + y)$ and $9(2y)$ in Example 31 should be noted.

Example 32

Remove the brackets from $9(x+2y)$ .

Solution

In the expression $9(x+2y)$ the $9$ must multiply both the $x$ and the $2y$ in the brackets. Thus

$\begin{align*} 9(x+2y) &= 9x + 9(2y)\\ &= 9x + 18 y \end{align*}$

Give any introductory information the student needs.

			Name	Type	Generated Value

q1consts	list	[ 8, -3, 3 ]
q1expr	expression	8(3x - 3q)
q1ans	expression	24x - 24q

			Name	Type	Generated Value

q2consts	list	[ -2, -6, 5 ]
q2var	string	f
q2expr	expression	8f*(3f - 3b)
q2ans	expression	24f^2 - 24fb

			Name	Type	Generated Value

q3consts	list	[ -6, 8 ]
q3expr	expression	-(-3*t + 3n)
q3ans	expression	3t - 3n

			Name	Type	Generated Value

q4sgns	list	[ "-", "-" ]
q4expr	expression	h*(-h - s)
q4ans	expression	-(h^2) - s*h
q4var	string	h

			Name	Type	Generated Value

q5consts	list	[ 2, -5 ]
q5expr	expression	(y + 2)*(-5)
q5ans	expression	-5y - 10

			Name	Type	Generated Value

alphabet

list

List of 21 items

Automatically regenerate variables?

Name

Data type

Value

xxxxxxxxxx
 
repeat(random(-9..9 except [-1,0,1]),3)

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Description

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

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Generated value: `list`

[ 8, -3, 3 ]

This variable doesn't seem to be used anywhere.

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Task 1:

$\var{q1expr}=\var{q1ans}$

Task 2:

$\var{q2expr}=\var{q2ans}$

Task 3:

$\var{q3expr}=\var{q3ans}$

Task 4:

$\var{q4expr}=\var{q4ans}$

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1.3.2. Removing Brackets from a(b+c) and a(b-c)

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Merryn Horrocks 1 year, 10 months ago

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Removing Brackets from expressions $a(b+c)$ and $a(b-c)$

Key Point 14

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1.3.2. Removing Brackets from a(b+c) and a(b-c)

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Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

Contributors

Feedback

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Comment

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Merryn Horrocks 1 year, 10 months ago

Merryn Horrocks 2 years, 10 months ago

Merryn Horrocks 2 years, 10 months ago

Removing Brackets from expressions a(b+c)a(b+c) and a(b−c)a(b-c)

Key Point 14

Error in variable testing condition

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Warning

Generated value: list

Parts

Mathematical expression

Advanced settings

Checking accuracy

Variable value generators

Pattern restriction

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Removing Brackets from expressions $a(b+c)$ and $a(b-c)$

Generated value: `list`