Year 10
An algebraic expression is a statement using symbols.
Expressions need to be written as simply as possible.
There are rules that should be followed:




A multiplication sign is not used eg. r x s = rs
The number part is written first in an expression
eg. y x 5 = 5y
Letters are written in alphabetical order when multiplying
eg. 5a x g x d = 5adg
3p
Divisions are written as fractions eg. 3p ÷ s =
s
Algebra is used to express rules using symbols. A
letter is used to stand for a number. The letter is
placed into a formula to explain what happens.
e.g. Write the following as a mathematical expression:
The sum of all the angles in a polygon is calculated by
subtracting two from the number of sides and multiplying
this number by 180°
S = (n – 2) × 180°
BETA:
Ex 7.01 pg 208
Ex 7.02 pg 209 - 212

Substitution means replacing a symbol with a
value. Remember to follow the rules of BEDMAS.
e.g.
Calculate the value of these expressions:
7x – 1 when x = 2
=72–1
= 14 – 1
fg
= 13
2
=
26
2
when f = 2 and g = 6
=4
5x2 - 3x + 2 when x = -3
= 5x(-3)2 - 3  -3 + 2
= 45 - −9 + 2
= 56
BETA:
Ex 7.03 pg 215
Ex 7.04 pg 216
Ex 7.05 pg 218
When multiplying terms all numbers and
variables can be combined.
e.g. Simplify:
3a x 4b
=12ab
-5c
x 6d x -2e
= 60cde
BETA:
Ex 8.01.pg 231
Homework book:
Ex C pg 75


Like terms can be added or subtracted, if they
are the same term and of the same power
The sign (+ or -) belongs to the number or
variable after it.
e.g.
Simplify
3a + a – 2a = 2a
4b – 7b + 2b = -b
7c + 5d – 9c + 2d = -2c + 7d
5ef + 6fg – 8fe + 7hg = -3ef + 6fg + 7gh

When we add and subtract like terms with
powers, we do not change the powers.
e.g. Simplify:
k3 – k2 + 3k + 4k3 – 6k2
= 5k3 – 7k2 + 3k
BETA:
Ex 8.02 pg 232
Ex 8.03 pg 233
Homework book:
Ex B pg 73
exponent,
power
y
xn means use ‘x’ as a factor n times.
e.g. p x p x p = p³
Multiplication
When multiplying numbers with
the same base, add the powers.
base
xm . xn = xm  n
e.g. 22 x 23 = (2 x 2) x (2 x 2 x 2)
= 25 (22+3)
y3 x y4 = y7
BETA:
Ex 8.05 pg 242
Ex 8.06 pg 245
Ex 8.07 pg 246
3q x 7q = 21q2
6r3 x 5r2s = 30r5s
x
When simplifying the square root of an algebraic
expression

take the square root of the number

divide the power of each variable by 2.
Examples: Simplify:
36 =
x
4
64 x y
6
10
66 = 6
= x 3 .x 3 = x3
= 64  x42  y102
= 8x2y5
142  y82
=

x
16
16 x y
= 8x7y4
14
8
BETA:
Ex 8.08 pg 248
Note 7: Expanding Brackets
• To expand brackets:
– Multiply the outside term by everything inside the
brackets
BETA:
– Simplify where possible
e.g.
Expand and Simplify:
a.) 4(x + 2) = 4x + 8
b.) −6(3x – 1) = −18x + 6
c.) x(2x – 3) = 2x2 − 3x
Ex 9.01 pg 253
Ex 9.02 pg 254
Ex 9.03 pg 255
d.) 5x – 2(6 +3x)
= 5x – 12 −6x
= −x – 12
e.) 4(2x – 7) −2(6 −x)
= 8x – 28 −12 +2x
= 10x − 40
Note 8: Factorising
BETA: Pg 257 onwards
Ex 9.04, 9.05, 9.06, 9.07
• Factorising is the opposite of expanding – putting brackets
back into the algebraic expression:
• Look for the highest common factor in the numbers and
place it outside the brackets.
• Look for any variables (letters) that are common. Take the
lowest power and place it outside the brackets.
e.g.
Factorise:
a.) 4a + 4b = 4(a+b)
d.) 6x + 21
= 3(2x +7)
b.) 3p – 3q + 3r = 3(p – q +r)
c.) 4x + 8y + 12x = 4(x + 2y + 3z)
e.) 24x - 32
= 8(3x – 4)