1. Starter Multiply the following 2a x 3b 3s x 4t 4d x 6d 3a x a x b
5y x 4z x y

2. Expanding brackets Learning Objectives: Key Words
To be able to expand brackets in algebra.
Key Words
Expanding
Expression
Algebra
brackets

3. L.O : To be able expand brackets in algebra.+4

4. L.O : To be able expand brackets in algebra.+3

5. L.O : To be able expand brackets in algebra.

6. L.O : To be able expand brackets in algebra.
3(2d-3e)
3 (2d-3e) = 6d
-9e

7. L.O : To be able expand brackets in algebra.
7a(2b-3c)
7a (2b-3c) =
14ab
-21ac

8. L.O : To be able expand brackets in algebra.
Expand the following brackets
4(2a+4)
5(3b-c)
3(4b-2c)
6(3h-4k)
8( 3r-2q-s)
Answer
8a+16
15b-5c
12b-6c
18h-24k
24r-16q-8s

9. Expanding brackets and simplifying
Expand and simplify:
2(3n – 4) + 3(3n + 5)
We need to multiply out both brackets and collect together like terms.
2(3n – 4) + 3(3n + 5) = 6n
– 8
+ 9n
+ 15
In this example, we have two sets of brackets. The first set is multiplied by 2 and the second set is multiplied by 3.
We don’t need to use a grid as long as we remember to multiply every term inside the bracket by every term outside it.
Talk through the multiplication of (3n – 4) by 2 and (3n + 5) by 3.
Let’s write the like terms next to each other.
When we collect the like terms together we have 6n + 9n which is 15n and – = 7.
= 6n + 9n –
= 15n + 7

10. Merit Question 5 Minutes
Expand and simplify:
5(3a + 2b) – a(2 + 5b)
We need to multiply out both brackets and collect together like terms.
5(3a + 2b) – a(2 + 5b) =
15a
+ 10b
– 2a
– 5ab
Here is another example with two sets of brackets. The first set is multiplied by 5 and the second set is multiplied by minus a.
Talk through the multiplication of (3a + 2b) by 5.
Next we need to multiply (2 + 5b) by –a. Talk through this.
= 15a – 2a + 10b – 5ab
NB: (negative × positive = negative)
-a × 5b = -5ab
= 13a + 10b – 5ab