Difference Between Expansion and Factorisation

Expanding and factoring are two terms that are widely heard of in Mathematics. However, some are not able to distinguish between them nor understand the meaning of these 2 terms.
Take for example,


















Thus, in this blog, I will be using some examples to highlight the differences between them.

Let's start by understanding what is factorisation first... ...

Factorisation is the process of writing an algebraic expression as a product of its factors.

For example:

The common factor for the 2 terms are 5, hence 5 is taken out.

Here are more examples:

This is just one method of factorisation. There are many other factorisation techniques, including:
grouping, using algebraic identities and inspection.


Moving on to expansion... ...

Expansion is the process of removing brackets and multiplying them term by term before consolidating the terms together.

For example:

There are also also algebraic identities that can be used as shown below:



Hopefully with a better understanding of what facotrisation and expansion is all about, I shall now move on to discuss the differences between the 2.

The factorised expression is more compact as it takes out common factors, thus it is useful when we are interested to compare terms that may have common factors. Also, in this expression, it can be used directly to solve quadratic equations to find the y-intercept (i.e. to let the expression equal to 0)

The expanded form shows every term present, thus we can see the order of the equation directly. The expanded form is required if we are required to add or subtract equations from one another e.g. when carrying out simultaneous equations.




References:

http://www.differencebetween.net/business/finance-business-2/difference-between-expanding-and-factoring/