1. Algebra Skills
Year 10

2. Note 1: Expressions
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
Divisions are written as fractions eg. 3p ÷ s =

3. Note 1: Expressions S = (n – 2) × 180°
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 pg 208
Ex pg

4. Starter: simplify the following expressions

6. Note 2: Substitution = 4 = 7x – 1 when x = 2 = 7  2 – 1 = 14 – 1 = 13
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
= 13
when f = 2 and g = 6
= 4 =

7. Note 2: Substitution
5x2 - 3x + 2 when x = -3 = 5x(-3)2 - 3  = 45 - −9 + 2 = 56
BETA:
Ex pg 215
Ex pg 216
Ex pg 218

8. Note 3: Simplifying Multiplication
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

9. Note 4: Adding and Subtracting Like Terms
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 =
4b – 7b + 2b =
7c + 5d – 9c + 2d =
5ef + 6fg – 8fe + 7hg = 2a -b
-2c + 7d
-3ef + 6fg + 7gh

10. Note 4: Adding and Subtracting Like Terms
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 pg 232
Ex pg 233
Homework book:
Ex B pg 73

11. an Note 5: Powers e.g. 22 x 23 = (2 x 2) x (2 x 2 x 2) = 25 (22+3) y7
exponent,
power
base 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.
e.g. 22 x 23 = (2 x 2) x (2 x 2 x 2)
= (22+3)
y3 x y4 = y7
BETA:
Ex pg 242
Ex pg 245
Ex pg 246
3q x 7q =
21q2
6r3 x 5r2s =
30r5s

12. Note 6: Square Roots = 6 = = x3 =  x42  y102 = 8x2y5 = 8x7y4
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: =
= 6 =
= x3 =
 x42  y102
= 8x2y5
=  x142  y82
BETA:
Ex 8.08 pg 248
= 8x7y4

13. Note 7: Expanding Brackets
To expand brackets:
Multiply the outside term by everything inside the brackets
Simplify where possible
e.g. Expand and Simplify:
a.) 4(x + 2)
b.) −6(3x – 1)
c.) x(2x – 3)
BETA:
Ex pg 253
Ex pg 254
Ex pg 255
= 4x + 8
d.) 5x – 2(6 +3x)
= 5x – 12 −6x
= −18x + 6
= −x – 12
e.) 4(2x – 7) −2(6 −x)
= 2x2 − 3x
= 8x – 28 −12 +2x
= 10x − 40

14. Note 8: Factorising d.) 6x + 21 = 4(a+b) = 3(2x +7) = 3(p – q +r)
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
b.) 3p – 3q + 3r
c.) 4x + 8y + 12x
d.) 6x + 21
= 4(a+b)
= 3(2x +7)
= 3(p – q +r)
e.) 24x - 32
= 4(x + 2y + 3z)
= 8(3x – 4)