§1.3 Multiplying, Adding and Subtracting Powers

C1 Arithmetic with Letters

Mr. Fintelman (FNL)

Wednesday September 25th

2024

1 / 18

Slide 1: Slide

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This lesson contains 18 slides, with text slides.

Lesson duration is: 90 min

Items in this lesson

C1 Arithmetic with Letters

Mr. Fintelman (FNL)

Wednesday September 25th

2024

Slide 1 - Slide

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...

Slide 2 - Slide

I can already…

… simplify fractions with letters.
… add and subtract fractions with letters.
… multiply and divide fractions with letters.

Prior Knowledge

Slide 3 - Slide

After this lesson, I can...

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

Goals

Slide 4 - Slide

Multiplying variables

x \cdot x \cdot x = . . .

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

x \cdot x \cdot y = . . .

Slide 5 - Slide

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

Slide 6 - Slide

Multiplying powers

x^{​ 2 ​ ​} \cdot x^{​ 2 ​ ​} = . . .

y^{​ 3 ​ ​} \cdot y^{​ 4 ​ ​} = . . .

3 x^{​ 2 ​ ​} \cdot 2 x^{​ 2 ​ ​} = . . .

Slide 7 - Slide

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 = . . .

3 x^{​ 2 ​ ​} \cdot 2 x^{​ 2 ​ ​} = 3 \cdot x \cdot x \cdot 2 \cdot x \cdot x = . . .

Slide 8 - Slide

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 ​ ​}

3 x^{​ 2 ​ ​} \cdot 2 x^{​ 2 ​ ​} = 3 \cdot x \cdot x \cdot 2 \cdot x \cdot x = 6 x^{​ 4 ​ ​}

Slide 9 - Slide

The product of powers

Slide 10 - Slide

Like terms

4 a + 6 a = . . .

8 a - 3 a = . . .

7 a b - 5 a = . . .

Slide 11 - Slide

Like terms

4 a + 6 a = 10 a

8 a - 3 a = 5 a

7 a b - 5 a = k . n .

Slide 12 - Slide

Like terms

4 a^{​ 4 ​ ​} + 6 a^{​ 4 ​ ​} = 10 a^{​ 4 ​ ​}

8 a^{​ 7 ​ ​} - 3 a^{​ 7 ​ ​} = 5 a^{​ 7 ​ ​}

7 a^{​ 5 ​ ​} - 5 a^{​ 2 ​ ​} = k . n .

Slide 13 - Slide

Simplifying brackets

2 a^{​ 2 ​ ​} (3 a - 4 b) = . . .

(a - 1) (a^{​ 2 ​ ​} + a) = . . .

Slide 14 - Slide

Simplifying brackets

2 a^{​ 2 ​ ​} (3 a - 4 b) =

(a - 1) (a^{​ 2 ​ ​} + a) =

6 a^{​ 3 ​ ​} - 8 a^{​ 2 ​ ​} b

a^{​ 3 ​ ​} + a^{​ 2 ​ ​} - a^{​ 2 ​ ​} - a = . . .

Slide 15 - Slide

Simplifying brackets

2 a^{​ 2 ​ ​} (3 a - 4 b) =

(a - 1) (a^{​ 2 ​ ​} + a) =

6 a^{​ 3 ​ ​} - 8 a^{​ 2 ​ ​} b

a^{​ 3 ​ ​} + a^{​ 2 ​ ​} - a^{​ 2 ​ ​} - a =

a^{​ 3 ​ ​} - a

Slide 16 - Slide

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: -

Slide 17 - Slide

Now I can...

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

Reflection

Slide 18 - Slide

§1.3 Multiplying, Adding and Subtracting Powers

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