1. Expanding Brackets

2. Objectives
By the end of the lesson you must understand what it is to multiply out (or expand) brackets.
By the end of the lesson you should feel confident about your ability to multiply out brackets successfully. For example you should be able to multiply out the following:
4(x + 7) = 3(y – 5) =
6a(a + 2) = 2b(3 – 2b) =

3. Mental Arithmetic
35 x 7 = ?

4. Mental Arithmetic
35 x 7 = 245
How did you work it out?

5. Mental Arithmetic
35 x 7 =
(30 + 5) x 7 =
30x7 + 5x7 = =
245

6. Mental Arithmetic
5 x 99 = ?

7. Mental Arithmetic
5 x 99 = 495
How did you work it out?

8. Mental Arithmetic
5 x 99 =
5 x (100 – 1) =
5x100 – 5x1=
500 – 5 =
495

9. Can you find the area of this rectangle (in your head)?
27cm
8cm
160cm2
56cm2
20cm
7cm
Answer: 216 cm2

10. What is the area of this rectangle?
x cm
7 cm
Answer: 7x cm2

11. What is the area of this rectangle?
Can you write your answer in two different ways?
a + 5 cm 20
4 cm 4a a 5
Answer: 4(a + 5) cm or 4a + 20 cm2
So 4(a + 5) = 4a + 20

12. Expanding Brackets
4(a + 5) = 4a + 20
4(a + 5) =
4xa + 4x5 =
4a + 20

13. Examples Try these on your whiteboard

14. Expanding Brackets Examples With Negative Numbers
x(x – 5) =
2a(3a – 4b) =
7x – 21
10x – 20
-9x – 15
-8x + 6
-x + 7
x2 – 5x
6a2 – 8ab

15. Examples Try these on your own
2(b – 7) =
7(s – 5) =
8(m – 3) =
-6(x + 5) =
-5(w + 2) =
-8(y – 3) =
-(x + 3) =
x(x + 1) =
x(x – 4) =
2x(x - 2) =
5d(8 + d) =
3x(2x + 3) =
4a(3 – 4a) =
k(k - l) =
2b(3a – 5b) =

16. Answers 6x2 + 9x 3a – 12 x2 + x 2b – 14 x2 – 4x 7s – 35 2x2 – 4x
8m – 24
-6x – 30
-5w – 10
-8y + 24
-x – 3
x2 + x
x2 – 4x
2x2 – 4x
40d + 5d2
6x2 + 9x
12a – 16a2
k2 – lk
6ab – 10b2

17. Objectives
By the end of the lesson you must understand what it is to multiply out brackets or expand brackets.
By the end of the lesson you should feel confident about your ability to multiply out brackets or expand brackets succesfully.

18. Check Your Understanding
4(x + 7) =
3(y – 5) =
6a(a + 2) =
2b(3 – 2b) =
4x + 28
3y – 15
6a2 + 12a
6b – 4b2