Name of Lecturer: Mr. J.Agius
Course: HVAC1
Lesson 27
Chapter 6: Algebra

Sequence of Mixed Operations on Algebraic Quantities
Since Algebraic Quantities contain symbols (or letters) which represent numbers the
sequence of operations is exactly the same as used with numbers.
Remember the word BODMAS which gives the initial letters of the correct sequence i.e.
Brackets, Of, Divide, Multiply, Add, Subtract.
Example 1
Simplify 2x2 + (12x4 – 3x4) ÷ 3x2 – x2
Answer
2x2 + (12x4 – 3x4) ÷ 3x2 – x2 = 2x2 + 9x4 ÷ 3x2 – x2
= 2x2 + 3x2 – x2
= 4x2

Brackets
Brackets are used for convenience in grouping terms together. When removing brackets
each term within the bracket is multiplied by the quantity outside the bracket:
Example 2
Remove the brackets in the following:
a
d
3(x + y)
m(a + b)
b
e
5(2x + 3y)
3x(2p + 3q)
c
f
4(a – 2b)
4a(2a + b)
Answer
a)
3(x + y)
= 3x + 3y
b)
5(2x + 3y)
= 5 × 2x + 5 × 3y
= 10x + 15y
c)
4(a – 2b)
= 4 × a – 4 × 2b
= 4a – 8b
d)
m(a + b)
=m×a+m×b
= ma + mb
e)
3x(2p + 3q)
= 3x × 2p + 3x × 3q
= 6xp + 9xq
f)
4a(2a + b)
= 4a × 2a + 4a × b
= 8a2 + 4ab
When a bracket has a minus sign in front of it, the signs of all the terms inside the bracket
are changed when the bracket is removed. The reason for this rule may be seen from the
following examples:
6 Algebra
Page 1
Name of Lecturer: Mr. J.Agius
Course: HVAC1
Example 3
Remove the brackets in the following:
a
– 3(2x – 5y)
b
– (m + n)
c
– (p – q)
d – 2(p + 3q)
Answer
a) – 3(2x – 5y)
= (– 3) × 2x – (– 3) × 5y
b) – (m + n)
=–m–n
c) – (p – q)
=–p+q
d) – 2(p + 3q)
= – 2p – 6q
= – 6x + 15y
When simplifying expressions containing brackets first remove the brackets and then add
the like terms together.
Example 4
Simplify:
a
(3x + 7y) – (4x + 3y)
b
3(2x + 3y) – (x + 5y)
c
x(a + b) – x(a + 3b)
d
2(5a + 3b) + 3(a – 2b)
Answer
a)
(3x + 7y) – (4x + 3y) = 3x + 7y – 4x – 3y
= 4y – x
b)
3(2x + 3y) – (x + 5y) = 6x + 9y – x – 5y
= 5x + 4y
c)
x(a + b) – x(a + 3b)
d)
2(5a + 3b) + 3(a – 2b) = 10a + 6b + 3a – 6b = 13a
6 Algebra
= xa + xb – xa – 3xb = – 2xb
Page 2
Name of Lecturer: Mr. J.Agius
Course: HVAC1
Brackets
Q1
Remove the brackets in the following:
1
/2 (x – y)
a
3(x + 4)
b
2(a + b)
c
3(3x + 2y)
d
e
5(2p – 3q)
f
7(a – 3m)
g
– (a + b)
h – (a – 2b)
i
– (3p – 3q)
j
– (7m – 6)
k
– 4(x + 3)
l
m – 5(4 – 3x)
n
2k(k – 5)
o
– 3y(3x + 4)
p a(p – q – r)
r
3x2(x2 -2xy + y2)
s
– 7P(2P2 – P + 1)
t
q
Q2
4xy(ab – ac + d)
– 2(2x – 5)
– 2m(– 1 + 3m – 2n)
Remove the brackets and simplify the following:
a
3(x + 1) + 2(x + 4)
b
5(2a + 4) – 3(4a + 2)
c
3(x + 4) – (2x + 5)
d
4(1 – 2x) – 3(3x – 4)
e
5(2x – y) – 3(x + 2y)
f
g
– (4a + 5b – 3c) – 2(2a + 3b – 4c)
h
2x(x – 5) – x(x – 2) – 3x(x – 5)
i
3(a – b) – 2(2a – 3b) + 4(a – 3b)
j
3x(x2 + 7x – 1) – 2x(2x2 + 3) – 3(x2 + 5)
6 Algebra
(
)
(
)
Page 3