1TH/vwo §11.3 Multiplication and addition

• Wiskunde
• Middelbare school
• havo, vwo
• Leerjaar 1

Here are the LIKE TERMS again, never leaving us alone.

However, recognising them makes your Maths life easier!

LIKE TERMS:

7 + 8 = 15            7 and 8 are like terms

7a + 8a = 15a     7a and 8a are like terms

        +             =                             and                             are like terms too!

7a​2​​

8a​2​​

7a​2​​

8a​2​​

15a​2​​

Task:  Try to find the final answer for the easiest one.

Remember your answer, because you won't see the task in the next slide!     Make a good use of LIKE TERMS!

The answer to the easiest one is:

1. 25
2. 50
3. 269
4. 250

Solution:

Did you notice that this task was all

about LIKE TERMS?

The terms 8 x         and

  2 x              are the like terms here.

They are added up, as you can see.

5​2​​

5​2​​

Solution:

Task: Which tasks(s) has LIKE TERMS: A, B or C?

Like terms are in:

1. A
2. B
3. C
4. A and C

Task:   Shorten formula A.   Give your answer 

in the next slide. 

Answer A

Task:   Shorten formula A.  

SOLUTION:

s=7t​2​​

A.   Intro to the coming THEORY (1)

Do you remember this, about shortening? 

          

This was taken from Ch 9. The same thing applies with squares!

Watch the next slide and be amazed.

1x=x

−1x=−x

1f=f

−1f=−f

  B. Intro to the next slide (2)

Basic rules:      1f = f    or     f = 1f          and        -1h = -h         or       -h = -1h

4f + 3f = 7f

4f + f = 4f + 1f = 5f

7d - d = 7d - 1d = 6d

Next we will look at similar calculations, only now with quadratic tasks!

Which one is true?

1. -1v = -v
2. v + v = v
3. -v -v = 2v
4. -v + v = 0

Solution:

A.     -1v = -v  is correct, because '1' can be left out

B.     v + v = v  is wrong, because v + v = 1v + 1v = 2v

C.     -v - v = 2v  is wrong, because -v -v = -1v -1v = -2v

D.     -v + v = -1v + 1v = 0  is correct

Solve both questions below.

Answer in next slide.

1. 4 t squared and 8
2. 5 t squared and 8 + 8 a squared
3. 5 t squared and 8
4. 4 t squared and 8 - 8 a squared

Solution:

Solve the task.

key in in next slide.

Solution:

Solve the task below.

Answer in next slide.

Shorten AS MUCH as you can!

1. y = - 13 x squared - 4
2. y = 13 x squared - 4
3. y = 13 x squared + 4
4. y = x squared - 4

SOLUTION:

Shorten AS MUCH as you can!

Below you see exercise 20 from §11.3

How to solve this exercise?

-see next slide too!-

How to solve this exercise? Like this:

FIRST WORK THEM OUT; ONLY THEN YOU CAN MAKE PAIRS!

FIRST WORK THEM OUT; ONLY THEN YOU CAN MAKE PAIRS!

Okay, let's do a bit together now:

1.                          x                =

So now it is obvious that  formula 1 and formula 7  are equal!

When doiung 20 for homework, work them all out and only then combine them!

p=k

k

k​2​​

Homework time.

Do §11.3 now.

+ H/V      you may skip: 15 and 16

+ VWO:  Do:     you may SKIP 15, 16, 17 and 18 

                             but   DO C4+C5