2TH §5.2 Removing double brackets

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• Middelbare school
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• Leerjaar 2

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Which exercises/theories should we discuss on the board?

Today's program

Questions about the homework? §5.1 exercises S4, 4, 5 and 6

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Refresh: Removing single brackets

New theory: Removing double brackets

Removing single brackets

In §5.1 you learned how to write a formula such as y = 2t(3t + 4) without brackets, by thinking of the formula as the area of a rectangle with a side of 2t and a side of 3t + 4.

You could also work this out with a multiplication table or by drawing arcs.

               Rectangle                             Multiplication table             Arcs

• Draw arcs to show what multiplication you're doing.
• Work this out on a peace of paper and give it to your teacher

Removing double brackets

In the same way, you can write formulas such as y = (2t + 3)(3t + 4) without brackets. Think of a rectangle with a side of 2t + 3 and a side of 3t + 4.

Removing double brackets

What should be written in the 

blue rectangle?

                                                                                                   I don't know

5t

6t

5t​2​​

6t​2​​

Removing double brackets

What should be written in the 

green rectangle?

                                                                                                   I don't know

6t

9t

6t​2​​

9t​2​​

Removing double brackets

The area is 

So 

can be written without brackets as

Removing double brackets

When removing brackets from formulas with negative numbers, you can use a multiplication table. Example: y = (2n - 7)(n + 1)

Put the 2n and -7 in the left column and n and 1 in the top row.

Removing double brackets

When removing brackets from formulas with negative numbers, you can use a multiplication table. Example: y = (2n - 7)(n + 1)

Put the 2n and -7 in the left column and n and 1 in the top row.

                           Fill in the table.

Removing double brackets

When removing brackets from formulas with negative numbers, you can use a multiplication table. Example: y = (2n - 7)(n + 1)

Put the 2n and -7 in the left column and n and 1 in the top row.

                           Fill in the table.      Write the formula as short                                                                                 as possible.

Removing double brackets

You can draw arcs to show what multiplications you are doing. This is sometimes called the "parrot beak" method (do you see the shape?). 

Example:

Which method should I use?

When being asked to write a formula without brackets, you can choose which method you use (rectangle, multiplication table, arcs, or something else). 

You do not have to show how you removed the brackets, but a rectangle/table or steps will show you know how to remove brackets, even if you make small mistakes.

HW Tuesday

 §5.2 Do exercises 9, 11, 12 and 13b

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