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Expansion and Factorisation
Monomials and Polynomials
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Expansion and Factorisation
Level of Difficulty: ¤¤
In this topic, you will learn how to expand, simplify and factorise polynomials.
Main Resource: Textbook Chapter 2
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.
Example and exercise on using algebraic tiles to do expansion.
Algebraic expansion using algebraic tiles.pdf
A generalisation of the algebraic tile method can be found in activity 1 on pg 34. In general, you should use
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:
Inspection or cross method
Difference of 2 squares
(A) Factorisation by Common Factor - recap of Sec 1's work
This video shows describes how to factorise an expression using Common Factor:
Worksheet 1 on Common Factor and Grouping:
Factorisation by Common Factor and Grouping Worksheet 1.pdf
Solutions to Worksheet 1 Level 1:
Solutions to Factorisation by Common Factor and Grouping Level 1 Practice.pdf
(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
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:
Summary: View the powerpoint slides on Factorisation by Common Factor and Grouping:
Common Factor and Grouping.ppt
(C) Factorisation by Inspection - refer to
This method is used to factorise
Expressions of the form
ax^2 + bx + c
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
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:
JiTT 2 questions and misconceptions.pdf
(D) Factorisation by Difference of 2 Squares - refer to
This method is applied to binomials which involve a difference of 2 perfect squares. After factorisation, the
of x should be integers.
JiTT 1 Classwork.pdf
Questions/Misconceptions on Difference of 2 Squares:
JiTT 1 questions and misconceptions.pdf
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