§1.3 Multiplying, Adding and Subtracting Powers

• Wiskunde
• Middelbare school
• vwo
• Leerjaar 2

C1 Arithmetic with Letters

Mr. Fintelman (FNL)

Wednesday September 25th

2024

Date	Wednesday September 25th 2024
Paragraph	§1.3 Multiplying, Adding and Subtracting Powers
Pages from the handbook	Pag. 23-25
Subject	Multiplying, Adding and Subtracting Powers

Today is the day...

I can already…

1. … simplify fractions with letters.
   
2. … add and subtract fractions with letters.
   
3. … multiply and divide fractions with letters.

Prior Knowledge

After this lesson, I can...

1. … simplify a product of powers.
   
2. … simplify a sum and a difference between powers.

Goals

Multiplying variables

$$x\cdot x\cdot x=...$$

$$y\cdot y\cdot y\cdot y\cdot y=...$$

$$x\cdot x\cdot y=...$$

Multiplying variables

$$x\cdot x\cdot x=x^3$$

$$y\cdot y\cdot y\cdot y\cdot y=y^5$$

$$x\cdot x\cdot y=x^{2}y$$

Multiplying powers

$$x^2\cdot x^2=...$$

$$y^3\cdot y^4=...$$

$$3x^2\cdot 2x^2=...$$

Multiplying powers

$$x^2\cdot x^2=x\cdot x\cdot x\cdot x=...$$

$$y^3\cdot y^4=y\cdot y\cdot y\cdot y\cdot y\cdot y\cdot y=...$$

$$3x^2\cdot 2x^2=3\cdot x\cdot x\cdot 2\cdot x\cdot x=...$$

Multiplying powers

$$x^2\cdot x^2=x\cdot x\cdot x\cdot x=x^4$$

$$y^3\cdot y^4=y\cdot y\cdot y\cdot y\cdot y\cdot y\cdot y=y^7$$

$$3x^2\cdot 2x^2=3\cdot x\cdot x\cdot 2\cdot x\cdot x=6x^4$$

The product of powers

Like terms

$$4a+6a=...$$

$$8a-3a=...$$

$$7ab-5a=...$$

Like terms

$$4a+6a=10a$$

$$8a-3a=5a$$

$$7ab-5a=k.n.$$

Like terms

$$4a^4+6a^4=10a^4$$

$$8a^7-3a^7=5a^7$$

$$7a^5-5a^2=k.n.$$

Simplifying brackets

$$2a^2(3a-4b)=...$$

$$(a-1)(a^2+a)=...$$

Simplifying brackets

$$2a^2(3a-4b)=$$

$$(a-1)(a^2+a)=$$

$$6a^3-8a^{2}b$$

$$a^3+a^2-a^2-a=...$$

Simplifying brackets

$$2a^2(3a-4b)=$$

$$(a-1)(a^2+a)=$$

$$6a^3-8a^{2}b$$

$$a^3+a^2-a^2-a=$$

$$a^3-a$$

Worktime

• You work neatly by…
  
• … reading the theory (again) before asking a question to your classmate.
  
• … raising a hand before asking a question to the teacher.
  
• … if the teacher is busy, remember your question and move on.

Help:

Exercises: 42, 43, 45, 46 and 48.

Assignments:

Pages: 23-25

Exercises: 42, 43, 45, 46 and 48.

Assignments from the planning of WEEK 3:

Extra:

Exercises: -

Now I can...

1. … simplify a product of powers.
   
2. … simplify a sum and a difference between powers.

Reflection