Academic Skills Advice
Basic Algebra Summary
Writing Algebraic Expressions:
Write a sentence in maths instead of English by assigning letters to numbers.
Examples:
𝒙

A number divided by three: can be written as

Half of a number plus quarter of another number: can be written
𝟑
𝒙
𝟐
+
𝒚
𝟒
Simplifying Expressions:
An algebraic expression can be simplified by collecting all the ‘like terms’ together.
Example:
 Simplify the following: 3a (a – b) + 5ab
(First remove the bracket then simplify).
After multiplying out the brackets we have: 3a2 - 3ab + 5ab = 3a2 + 2ab
Factorisation:
An expression can be simplified by factorising it. This means taking out any common
factors (i.e. putting the brackets back in).
Example:

Simplify the following: 8𝑥 + 3𝑥𝑦 + 9𝑥𝑦 − 4𝑥 (First collect like terms then factorise).
Collect like terms:
Factorise:
4𝑥 + 12𝑥𝑦
4𝑥(1 + 3𝑦)
Functions:
Functions are another way of writing equations but using 𝑓(𝑥) or 𝑔(𝑥) etc instead of y.
e.g.:
𝑓(𝑥) = 3𝑥 − 4
OR
𝑓: 𝑥 → 3𝑥 − 4
They both mean the same thing (do 3 x 𝑥 then take away 4)
Examples:

Given the function: 𝑓(𝑥) = 5𝑥 + 2
Find 𝑓(6)
This just means wherever you see an 𝑥 replace it with a 6.
𝑓(𝑥) = 5𝑥 + 2
𝑓(6) = 5 × 6 + 2
𝑓(6) = 32
H Jackson 2011 / Academic Skills
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