2TH §5.1 Removing single brackets

• Wiskunde
• Middelbare school
• havo, vwo
• Leerjaar 2

1. Calculate the perimeter of the figure. Write your answer as short as possible.

2. Calculate the area of the figure. Write your answer as a single square root.

Entry Ticket

Starting with something new

Removing single brackets

Something like this .....  5(2+4)  =

Removing single brackets

5(2+4)=

          11                                   -1

          30                                 something else

Rectangles

You can think of the calculation 5(2+4) as working out the area of this rectangle.

Rectangles

The area of the rectangle is 

length x width =

5 x (2+4) = 

5(2+4)

Rectangles

 area rectangle = 5(2+4) = 5 x 6 = 30

You could also calculate the area of the

blue rectangle and red rectangle first 

and then add those up.

area rectangle = 5 x 2 + 5 x 4 =

                                    10 + 20 = 30

Rectangles with variables

If at least one of the sides of the rectangle is given as a variable, you can make a formula for the area of the rectangle.

Rectangles with variables

You can make a formula with brackets and one without.

Area rectangle = 5 x (t+4) = 5(t+4)

OR

Area rectangle = 5 x t + 5 x 4 =

                                    5t + 20

Rectangles with variables

Because both formulas give the same area, we now now that

5(t+4) = 5t + 20

We can use this to rewrite formulas

with brackets as formulas without

brackets.

Removing brackets

Write the formula y = 2(3t + 4) without brackets.

Removing brackets

Write the formula y = 2(3t + 4) without brackets.

Think of a rectangle with a side of 2 and a side of 3t + 4

Removing brackets

Write the formula y = 2(3t + 4) without brackets.

Think of a rectangle with a side of 2 and a side of 3t + 4

Area blue rectangle = 2 x 3t = 6t

Area red rectangle = 2 x 4 = 8

y = 6t + 8

Removing brackets

Instead of a rectangle, you can also use a multiplication table.

y = 2(3t + 4) = 6t + 8

More variables, negative numbers

If you want to write 2t(5t - 3) without brackets, it is hard to imagine a rectangle, because a lenght of -3 is not possible.

We can still  use a multiplication table!

More variables, negative numbers

Write y = 2t(5t - 3) without brackets.

What should be written over here?

            

7t

10t

7t​2​​

10t​2​​

More variables, negative numbers

Write y = 2t(5t - 3) without brackets.

What should be written over here?

            

−t

6t

−6t

2t−3

More variables, negative numbers

Write y = 2t(5t - 3) without brackets.

            

Notation

If a 1 is written in front of a variable or bracket, you do not write down the 1. 

Instead of 1p, you write p

Instead of -1t, you write -t

Instead of -1(5t+2), you write -(5t+2)

Homework Tuesday

§5.1 Do exercises S4, 4, 5, S6 and 6

Don't forget to check and correct your answers with the solutions book!