Expanding and Factorising – GCSE Maths
Introduction
Expanding:
- Simplifying the expression or equation by eliminating the brackets present. Multiplying the number outside the brackets with numbers inside.
Factorising:
- Writing the simplified equation in a brief form means using brackets.
Expansion and Factorisation in Detail
Expansion:
Example:
- Step#1: Identify the paranthesis in expression –
- Step#2: Apply the distributive property, multiply the term outside the paranthesis by the term inside –
- Step#3: Combine the terms with same variable if any –
Factorisation:
Example:
- Step#1: Find the common factors –
- Step#2: Combine the terms having common factors-
Expand the following algebric equations:
- These are also used as general formulae.
Solved Example
Solved ExampleProblem: Represent the multiplication of three consecutive integers in algebric form. Write the equation by expanding it further.
Solution:
Suppose x is an integer:
Final Answer: x3 + 3x2 + 2x = 0
Solved Example
Problem: What will be the total price of 2 sets of 5 toffees and 6 chocolates if the price individually is represented by variables?
Solution:
Suppose the price of one toffees is x and that of one chocolate is y, then the total price will be:
Final Answer: 10x + 12y
Solved Example
Problem: Suppose that there are total 5 baskets of Apples and 6 baskets of Bananas. If Bananas are 15 more than Apples, represent them in algebric form in both the expanded and factorised forms.
Solution:
If there are x number of apples in one basket then bananas will be x + 15, And we can represent the total number of Apples and Bananas in all the baskets as follows:
Solved Example
Problem: Suppose a person owns x no. of cows and horses 10 more than cows. similarly another person owns the y no. of cows and horses which are 15 more than the cows he owns. Then represent the total number of cows and horses these two persons own.
Solution:
It can be represented as:
