Expanding Brackets
Objectives:
D Grade
Multiply out expressions with brackets such as:
3(x + 2) or 5(x - 2)
Factorise expressions such as 6a + 8 and x2 – 3x
C Grade
Expand (and simplify) harder expressions with
brackets such as:
x(x2 - 5) and
3(x + 2) - 5(2x – 1)
Prior knowledge:
Understand that
2x means x + x
x2 means x × x
cab = abc because multiplication is commutable
Be able to collect terms
Use the grid method for multiplying
Expanding Brackets
What are brackets and why use them?
Example 1
3(xx + 33)
A number or letter / term next to
brackets means 3 of whatever is
in the brackets
Collecting terms we have:
In other words:
3x + 9
3 × (xx + 3)
3
×
This can be put into the grid method
3x
Using the grid method we add the answers in the grid
Because 3x and 9 have different powers of x
(there is no x in the term 9) we leave the answer as it is
9
+
Expanding Brackets
Example 2
x × (xx + 33)
Remember x × x =
×
x2
x2
Example 3
3x
+
x × (xx2+ 33)
Remember x ×
x2 =
x3
×
x3
3x
+
Expanding Brackets
Now do these:
1. 2(x + 3) 2. 2(t + 1)
3. 3(d − 4)
4. −2(x + 1)
-2x - 2
2t + 2
3d - 12
2x + 6
5. 4(y + 4)
6. 6(h − 2)
7. 5(3ab + 2a)
8. − 3(p − 2)
-3p - 6
6h - 12
15ab+ 5a
4y + 16
9. p(p + 2) 10. b(2b + 3) 11. w(2w − 3)
12. t(3t − 4)
2b2 + 3b
2w2 – 3w
p2 + 2p
3t2 – 4t
13. p(p2 + 4)
14. w(w2 − 3)
15. x(xy − xy2)
w3 – 3w
p3 + 4p
x2y + x 2y 2
16. ct2 (t − 3)
17. fp(p3 − p)
18. xyz(xz + yz)
fp4 – fp2
ct3 – 3ct 2
x2yz 2 + xy2 z2