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

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

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

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

9. Step 3 2a +3 4a
8a2
+12a +2
+4a +6
So we have
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
Multiply the individuals components together
(3b + 2)(4b – 6) 3b +2 4b -6

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

18. Step 3 2a +3 4a
12b2
+8b +2
-18b
-12
So we have
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:
(2a + 7)(6a + 2)
(4b + 5)(3b +9)
(5c + 4)(8c – 2)
(7d + 5)(3d – 4)
(9y –2)(3y + 6)
(4p – 3)(2p – 6)
(8m – 2)(7m – 4)

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

22. Did you get them correct?
(2a + 7)(6a + 2)
(4b + 5)(3b +4)
(5c + 4)(8c – 2)
(7d + 5)(3d – 4)
(9y –2)(3y + 4)
(4p – 3)(2p – 6)
(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. Be able to expand brackets and simplify the expressions that arise
THINK!
Did you meet the objective of the lesson?
Be able to expand brackets and simplify the expressions that arise