Expansion

Recall that only like terms (e.g. 4x and 9x are like terms. 4x and 9y are unlike terms) can be added or subtracted.
The process of removing brackets from an algebraic expression and writing the result term by terms is called expansion of algebraic expressions.

For the expansion of the product of two algebraic expressions, we multiply each term in the first expression by each term in the second expression. 
E.g. (a + b)(c + d) = ac + ad + bc + bd

The image below shows the general formulas for the expansion of algebraic expressions: 

Factorisation

Factorisation is the reverse process of expansion, as it involves writing an algebraic expansion as a product of its factors. The methods of factorisation are: 

1. Factorising by extracting common factors
ab + ac = a(b + c)

2.Factorisation by grouping
ax + ay + bx + by = a(x + y) + b(x + y) = (x + y)(a + b) 

3. Factorisation by using algebraic identities
a2 ± 2ab + b2 = (a ± b)2
a2 - b2 = (a + b)(a - b)

Factorisation of Quadratic Expressions

Quadratic expressions are of the form ax2 + bx + c where a, b and c are real numbers and a ≠ 0. The highest power of x in a quadratic expression is 2. To factorise a quadratic expression, we express it as a product of 2 factors where each factor is not equal to 1. 

The cross method can be used to factorise a quadratic expression. Do watch the following video to learn how this is done:

Factorisation of Quadratic Equations by Factorisation

Quadratic expressions are of the form ax2 + bx + c where a, b and c are real numbers and a ≠ 0. The highest power of x in a quadratic expression is 2. To factorise a quadratic expression, we express it as a product of 2 factors where each factor is not equal to 1. 

The cross method can be used to factorise a quadratic expression. Do watch the following video to learn how this is done:

How To

In the formula V = πr2h, V is the subject of the formula. The subject appears by itself on the left-hand side of the formula and nowhere else. r and h can also be made the subject of the formula. For example, h = V/πr2.

To make a variable the subject of the formula, we rearrange the formula so that only that particular variable appears on the left-hand side of the formula. 

Remember that whatever you do to one side of the equation, you have to do the same to the other side. Watch the following video for a simple example of how this is achieved.