1. Objective
Be able to expand
brackets and simplify
the expressions that
arise

2. Question (Level 6)
• Expand and simplify the following
expression
(2a + 3)(4a + 2)

3. Step 1
(2a + 3)(4a + 2)
2a +3
4a
+2
Multiply the
individuals
components together

4. 2a +3
4a 8a2
+2

5. 2a +3
4a 8a2
+12a
+2

6. 2a +3
4a 8a2
+12a
+2 +4a

7. 2a +3
4a 8a2
+12a
+2 +4a +6

8. Step 2
• Now collect the like terms
2a +3
4a 8a2
+12a
+2 +4a +6
16a

9. Step 3
So we have
2a +3
4a 8a2
+12a
+2 +4a +6
8a2
+ 16a + 6

10. This will always work!
You may have to deal
with negatives too,
but don’t worry it’s
just as easy.

11. Dealing with negatives
Expand and simplify the following
expression
(3b + 2)(4b – 6)

12. Step 1
(3b + 2)(4b – 6)
3b +2
4b
-6
Multiply the
individuals
components together

13. 3b +2
4b 12b2
-6

14. 3b +2
4b 12b2
+8b
-6

15. 3b +2
4b 12b2
+8b
-6 -18b

16. 3b +2
4b 12b2
+8b
-6 -18b -12

17. Step 2
• Now collect the like terms
2a +3
4a 12b2
+8b
+2 -18b -12
-10b

18. Step 3
So we have
2a +3
4a 12b2
+8b
+2 -18b -12
12b2
–10b – 12

19. That’s it!
Just be careful when
you are multiplying
negative numbers
and take your time
when collecting like
terms.

20. Let’s try some questions –
You only have five minutes!
• Expand and simplify:
1) (2a + 7)(6a + 2)
2) (4b + 5)(3b +9)
3) (5c + 4)(8c – 2)
4) (7d + 5)(3d – 4)
5) (9y –2)(3y + 6)
6) (4p – 3)(2p – 6)
7) (8m – 2)(7m – 4)

21. Time is up!
Let’s check some
answers

22. Did you get them correct?
1) (2a + 7)(6a + 2)
2) (4b + 5)(3b +4)
3) (5c + 4)(8c – 2)
4) (7d + 5)(3d – 4)
5) (9y –2)(3y + 4)
6) (4p – 3)(2p – 6)
7) (8m – 2)(7m – 4)
12a2
+ 46a +14
12b2
+ 31b +20
40c2
+22c - 8
21d2
– 13d -20
27y2
+30y - 8
8p2
–30p + 18
56m2
– 46m +8

23. THINK!
Did you meet the objective of
the lesson?
Be able to expand brackets
and simplify the expressions
that arise