§1.1 Expanding Brackets - PART 1

C1 Arithmetic with Letters
Mr. Fintelman (FNL)
Wednesday September 4th
2024

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C1 Arithmetic with Letters
Mr. Fintelman (FNL)
Wednesday September 4th
2024

Slide 1 - Tekstslide

Date
Wednesday September 4th 2024
Paragraph
§1.1 Expanding Brackets
Pages from the handbook
Pag. 12-14
Subject
Rules:
a(b + c) = ab + ac
(a + b)(c + d) = ac + ad + bc + bd
Today is the day...

Slide 2 - Tekstslide

I can already…
  1. … simplify products with letter variables.
  2. … simplify additions and subtractions with letter variables.
  3. … collect like terms to simplify letter variables.
  4. … simplify letter variables by applying the order of operations.

Prior Knowledge

Slide 3 - Tekstslide

Examples of letter variables

Slide 4 - Tekstslide

After this lesson, I can…
  1. … simplify an expression with the following rule: a(b + c) = ab + ac
  2. … simplify an expression with the following rule: (a + b)(c + d) = ac + ad + bc + bd

Goals

Slide 5 - Tekstslide

Farmer Edward - Area of the land and the barn

Slide 6 - Tekstslide

Farmer Edward - Area of the land and the barn
Area I
Area II 
Total Area
=ABAE
=ABBE
=ABAE+ABBE

Slide 7 - Tekstslide

Farmer Edward - Area of the land and the barn
Area I
Area II
Total Area
=ab=ab
=ac=ac
=ab+ac=ab+ac

Slide 8 - Tekstslide

Farmer Edward - Area of the land and the barn
Area I
Area II
Total Area
=ab=ab
=ac=ac
=a(b+c)=ab+ac

Slide 9 - Tekstslide

More examples
2b(5a7)=
=10ab14b
=2b5a+(2b7)
=10ab+(14b)
Explain
In this rule we multiply the factor outside the brackets with both factors in the brackets.
So in this example we multiply 2b with 5a and 2b with -7.

If you find it difficult, it might help to 'split' the parts with brackets, this often helps with the rule of 'two negatives makes it positive'.

Slide 10 - Tekstslide

More examples
(3p2q)=
=3p+2q
=13p+(12q)
=3p+(2q)
Explain
Again you multiply factors, but in this case we see an 'invisible -1'.
This is another example in which it might help to 'split' the parts with brackets, because negative numbers often lead to mistakes for starters.

Slide 11 - Tekstslide

More examples
83(2ab)=8+(32a)+(3b)=
=8+(6a)+(3b)
=86a+3b
=8+(32a)+(3b)
Explain
Here we see a longer example, in which I 'split' the (-3) to make sure that I won't make mistakes later.
This is a tricky example.

Slide 12 - Tekstslide

According to the book
2b(5a7)=10ab14b
(3p2q)=3p+2q
83(2ab)=86a+3b
Explain
So if we go by the steps the book tells you, you'll see that the book doesn't show most steps.
I don't like that, this is one of the reasons why students often feel lost in this particular paragraph.

Slide 13 - Tekstslide

Farmer Charles - Area of the land and the barn

Slide 14 - Tekstslide

Farmer Charles - Area of the land and the barn
Total Area

Area I
Area II
Area III
Area IV
Total Area

=ab=ab
=a2=2a
=ab+2a+3b+6
=3b=3b
=32=6
=(a+3)(b+2)

Slide 15 - Tekstslide

More examples
(a+2)(b+5)=
=(ab)+(a5)+(2b)+(25)
=(ab)+(5a)+(2b)+(10)
=ab+5a+2b+10
Explain
This distribution is a little more, but not as different.
Now there are simply four factors, instead of three.

Slide 16 - Tekstslide

More examples
(c+2)(d4)=
=(cd)+(c4)+(2d)+(24)
=(cd)+(4c)+(2d)+(8)
=cd4c+2d8
Explain
But it is such longer distributions that make me want to use brackets to make sure I won't miss negative numbers.

Slide 17 - Tekstslide

More examples
(x+2)(x3)=
=(xx)+(x3)+(2x)+(23)
=(x2)+(3x)+(2x)+(6)
=x23x+2x6
=x2x6
Explain
If these factors share variables, you will often see that you need to simplify a bit more, by either adding or subtracting like terms.

Slide 18 - Tekstslide

According to the book
(x+2)(x3)=
x23x+2x6
=x2x6
(c+2)(d4)=
cd4c+2d8
(a+2)(b+5)=
ab+5a+2b+10
Explain
Here it is in short.

Slide 19 - Tekstslide

Worktime
You work neatly by…
  1. … reading the theory (again) before asking a question to your classmate.
  2. raising a hand before asking a question to the teacher.
  3. … if the teacher is busy, remember your question and move on.
Help:
Exercises: 2, 4, 5, 8 and 9
Assignments:
Pages: 10-11
Exercises: 4, 5, 6 and 9
Assignments from the planning of WEEK 1:
Extra:
Exercises: 7

Slide 20 - Tekstslide

Now I can...
  1. … simplify an expression with the following rule: a(b + c) = ab + ac
  2. … simplify an expression with the following rule: (a + b)(c + d) = ac + ad + bc + bd
Reflection

Slide 21 - Tekstslide