Worksheet 3.1 (page 1 of 3)
Expanding linear expressions
The following two examples show how AEM can be used to expand linear
expressions. The expansion is represented as finding the area of a rectangle,
width w, and length l, where Area = w × l.
The working frame is used for expanding algebraic expressions to separate the
blocks belonging to the question from those representing the answer. (Negative
terms are referred to as signed area, as area can not be a negative quantity.)
length
width
×
Example 1. Expand 2(x – 3)
This means 2 × (x – 3) or 2 lots of (x – 3).
The expansion is represented as finding the area of a rectangle with width 2, and
length x – 3.
Answer: 2(x – 3) = 2x – 6
CSF Sample Units: Years 8 to 10 Maths – Working with linear expressions
Worksheet 3.1 (page 2 of 3)
Example 2. Expand –2(x – 3)
Answer: –2(x – 3) = –2x + 6
1. Use your blocks and working frame to find the expansions of the following
expressions.
a) 3(x – 2)
i) 3(x – 4)
b) 4(x – 1)
j) 5(x + 2)
c) 5(x + 3)
k) 5(x – 2)
d) 6(x – 1)
l) –1(x + 3)
e) 2(x + 3)
m) –2(x + 3)
f) –1(x – 3)
n) –3(x + 3)
g) –2(x – 2)
o) –5(x – 4)
h) –4(x – 1)
p) –3(x – 5)
2. Write the expanded expression and the answer, for the following diagrams.
a)
c)
___ ( _______ ) = __________
___ ( _______ ) = ___________
CSF Sample Units: Years 8 to 10 Maths – Working with linear expressions
Worksheet 3.1 (page 3 of 3)
b)
d)
___ ( _______ ) = ____________
___ ( _______ ) = _________
Write the expansions of the following expressions.
Use your algebra blocks or diagrams to help where necessary.
e) 2(2x – 3)
f) 3(3x – 1)
g) 4(3x – 1)
h) 2(5x + 4)
i) 3(2x – 2)
j) 3(2 – 2x)
k) –2(2x – 1)
l) –5(2x + 2)
m) –3(2x – 3)
n) –2(4x – 5)
o) –3(1 – x)
p) –4(3 – 2x)
CSF Sample Units: Years 8 to 10 Maths – Working with linear expressions
CSF Sample Units: Years 8 to 10 Maths – Working with linear expressions