The document discusses expanding and simplifying expressions within brackets. It provides examples of multiplying out terms within brackets for expressions like (2a + 3)(4a + 2) and (3b + 2)(4b - 6). The key steps are to multiply out each corresponding term, then collect like terms. Distributing negatives requires being careful about the signs of multiplied terms. The document encourages practicing expanding several example expressions within time limits to check understanding.

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