Level of Difficulty: ¤¤

Unit 2: Expansion and Factorisation


In this topic, you will learn how to expand, simplify and factorise polynomials.

Main Resource: Textbook Chapter 2

Alternate Resource: http://www.algebralab.org/lessons/lesson.aspx?file=algebra_factoring.xml#4
This website has very good explanation of all the 4 methods of factorisation, as well as examples for you to try. You can check your solutions on the spot. The section on difference of 3 cubes is optional - you can have a look at it as an enrichment.

Part 1: Expansion of algebraic expressions

Read and understand A and B on pg 33.
We can use algebraic tiles to show how expansion works.

Watch this video to see how algebraic tiles is used in showing the concept of finding area in the process of expansion.


URL: http://www.youtube.com/watch?v=jxR0gyXFQwQ

Example and exercise on using algebraic tiles to do expansion.

A generalisation of the algebraic tile method can be found in activity 1 on pg 34. In general, you should use distributive law to work out the product/expansion of 2 algebraic expressions.

The textbook provides comprehensive examples. Read through as many as you need to get the concept.

Exercises: 2.1, 2,2
Extra Practice: Workbook Ch 2


Part 2: Factorisation of algebraic expressions

Factorisation is the opposite process of expansion. Instead of removing the brackets, we try to group terms together in brackets.

There are 4 methods of factorization:


(A) Factorisation by Common Factor - recap of Sec 1's work

This video shows describes how to factorise an expression using Common Factor:

URL: http://www.youtube.com/watch?v=NxZSyuRKSKI

Worksheet 1 on Common Factor and Grouping:
Solutions to Worksheet 1 Level 1:


(B) Factorisation by Grouping - recap of Sec 1's work

Factorisation by grouping is an extension to Common Factor.
In this case, usually there are 4 terms in the expression. You have to "group" them 2-by-2 together and factorise each group by taking out the common factor. This common factor should be the same for both groups so that you can combine them again in the final step.

This video demonstrates how to factorise by grouping:

URL: http://www.youtube.com/watch?v=LitM6ERl88A

Summary: View the powerpoint slides on Factorisation by Common Factor and Grouping:



(C) Factorisation by Inspection - refer to JiTT 2
This method is used to factorise Quadratic Expressions of the form ax^2 + bx + c, where a, b and c are constants.

The way of "visualising" the process is through algebraic tiles, which is explained in TB Pg 51. Remember that factorisation is the reverse of expansion so now we are given the "area" of the rectangle and we need to figure out the "dimensions".

For actual practice, we will use the "cross" method or Inspection.
The factors are obtained using trial and error, as shown on TB Pg 54 - 57. Not all quadratic expressions can be factorised. For now, we will just work with those that can.

Questions/Misconceptions on Inspection/Cross Method:


(D) Factorisation by Difference of 2 Squares - refer to JiTT 1
This method is applied to binomials which involve a difference of 2 perfect squares. After factorisation, the coefficients of x should be integers.

Classwork:

Questions/Misconceptions on Difference of 2 Squares: