Uncle Johan has a big farm. He wants to fence up this vegetable garden.

What is the area of this garden in terms of x? x2

He fences up the garden in the shape of a square with sides x meters long.

x

x

Jasmin, his daughter wants to plant some flowers.

Uncle Johan extends the fences by 3 meters to the east to make a bigger garden for the flowers.

x

x

3

The length of the new garden is

x + 3

x x2

What is the area of the new garden?

The width of the new garden is

x + 3

x

3x

x + 3

x x2 3xx2

The area of the garden is

x ( x + 3) = x2 + 3x

Mrs Johan wants a herbal garden. Uncle Johan then, extends the garden by 2 meters to the south.

x + 3

x x2

2

+

x + 3

x2

x

+

2

What is the area of Uncle Johan’s garden now?

x2 3x

2x2

x

2

3

6

x + 3

x2

x

+

2

x2 3x

2x 6

= x2 + 3x + 2x + 6 = x2 + 5x + 6

( x + 2) ( x + 3)

Expansion of Quadratic Expression:Method 1 : Area of rectangle

Expand (a + 1) (a + 4)

a + 4

a

+

1

a2 4a

a 4

(a + 1) (a + 4)

= a2 + a + 4a + 4

= a2 + 5a + 4

Using the “Area” method,expand:-

1. (x + 2) (x + 5)

2. (y + 8) (y + 1)

3. (a + 10)(a + 7)

( x + 2) ( x + 3)

+ 2 ( x + 3) ( x + 3) = x

+6

without using the areas of

rectangles

= x2 + 3x + 2x

= x2 + 5x + 6

This is known as

the “Distribut

ion Method”

( x + 5) ( x + 4)

+ 5 ( x + 4) ( x + 4) = x

= x2 + 4x + 5x + 20

= x2 + 9x + 20

( x – 7) ( x – 2)

= x2 - 2x - 7x + 14

= x2 - 9x + 14

- 7= x ( x – 2) ( x – 2)

Expand

1.(x + 6) (x + 2)

2.(a + 3) (a + 8)

3.(a – 4) (a – 1)

4.(x – 5) (x – 9)

5.(x + 5) (x – 3)

6.(a + 7) (a – 3)

( x + 3) ( x + 3)

( m + 10)2

( a – 5) (a – 5 )

= (a – 5)2

= ( x + 3)2

= (m + 10) ( m + 10)

( k – 8 )2

= ( k – 8 ) ( k – 8)

Expansion of Quadratic Expression:Method 3 : “Face”

(a + 4 ) ( a + 2 )

Expand (a + 4) (a + 2)

+ 4a + 2a + 8= a2

= a2 + 6a + 8

Expansion of Quadratic Expression:Method: “Face”

(x + 3 ) ( x + 4 )

Expand (x + 3) (x + 4)

+ 3x + 4x + 12= x2

= x2 + 7x + 12

Expansion of Quadratic Expression:Method 3 : “Face”

(x - 2 ) ( x - 8 )

Expand (x - 2 ) (x - 8)

- 2x - 8x +16= x2

= x2 – 10x + 16

Expansion of Quadratic Expression:Method 3 : “Face”

(x - 3 ) ( x + 2 )

Expand (x - 3 ) (x + 2 )

- 3x + 2x - 6= x2

= x2 – x – 6

( y + 11 ) ( y - 6 )

Expand (y + 11 ) (y – 6 )

+ 11y - 6y - 66= y2

= x2 + 5y – 66