The document provides examples of factorizing algebraic expressions. It begins with expanding simple expressions like 3g + 4 and finding the common factors of terms like 12 and 20. The next section provides more examples of factorizing expressions like x2 + 2x by finding the highest common factor. It emphasizes factorizing completely, like writing 3abc(ab4 + 9) instead of 9abc(ab4 + 9). The document concludes with an exercise for students to practice factorizing expressions and an extension with more challenging examples. It provides the opportunity for a 10 minute practice session to reinforce the steps of factorizing algebraic expressions.

1. Starter
Expand:
1. 3𝑔 𝑔 + 4
2. 𝑥2 𝑥 + 2
3. 𝑥2 𝑥 − 1
4. 2𝑎 3 + 𝑎 − 2(4𝑎 − 2)
5. ( 𝑥 + 3) ( 𝑥 – 3)
Find the common factors:
1. 12 and 20
2. 24 and 56
3. 4a and 12
4. 25𝑎2 and 15𝑎3

2. Starter
Expand:
1. 3𝑔2
+ 12𝑔
2. 𝑥3
+ 2𝑥2
3. 𝑥3
− 𝑥2
4. 2𝑎2
− 2𝑎 − 4
Find the common factors:
1. 4
2. 8
3. 4
4. 5𝑎2

3. Factorising Expressions
Thursday 5th November
Objectives:To be able to Factorise Expressions

4. Factorising – What does it mean?
2 𝑦 + 3 = 2𝑦 + 6
Expanding
Factorising – Reverse of expanding

5. Factorising – What does it mean?
2 𝑦 + 3 = 2𝑦 + 6
Expanding
Factorising
Factorising – Put in the brackets!

6. Factorising – How do we do it?
2𝑦2
+ 6𝑦
Look for the
highest common
factor
"2𝑦"
2𝑦(𝑦 + 3)
Take out the common
factors and put in the
brackets
Check the answer by
expanding it back out
again.

7. Factorise
Factorise: 12𝑥2
𝑦 + 6𝑥𝑦2
“3𝑥𝑦(4𝑥 + 2y)”

8. Factorise
Factorise: 12𝑥2
𝑦 + 6𝑥𝑦2
“3𝑥𝑦(4𝑥 + 2y)”
Is this wrong?

9. Factorise
Factorise: 12𝑥2
𝑦 + 6𝑥𝑦2
“6𝑥𝑦(2𝑥 + 𝑦)Is this wrong?

10. Factorise – Part 1
Factorise: 12𝑥2
𝑦 + 6𝑥𝑦2
“3𝑥𝑦(4𝑥 + 2y)”
“6𝑥𝑦(2𝑥2 + 𝑦2)"
Both are correct, why is it
different?
Factorised fully
Get used to
doing this

11. Look at these
What do you see?
Factorise completely : 3𝑎2
𝑏5
𝑐 + 27𝑎𝑏𝑐
9𝑎𝑏𝑐(𝑎𝑏4 + 9)
𝑎𝑏𝑐(3𝑎𝑏4 + 27)
3𝑎𝑏𝑐(𝑎𝑏4
+ 9)

12. Look at these
What do you see?
Factorise completely : 3𝑎2
𝑏5
𝑐 + 27𝑎𝑏𝑐
9𝑎𝑏𝑐(𝑎𝑏4 + 9)
𝑎𝑏𝑐(3𝑎𝑏4 + 27)
3𝑎𝑏𝑐(𝑎𝑏4
+ 9)
Changed the numbers to
common multiples
Not Fully Factorised
Correct answer

13. Exercise – Let’s get through this quick!
1. 2x + 10
2. 15 − 3m
3. 28 − 56n
4. 𝑥2
+ 2𝑥
5. 3𝑥2 − 9𝑥
6. 𝑥3 − 𝑥2
1. 12𝑦2
+ 8𝑦
2. 2𝑎2 − 𝑎
3. −7𝑥 − 8
4. ℎ2 − 25h
Extension:
1. ℎ2 − 25
2. 𝑥2 − 16
You have 10 minutes…

14. Exercise – Let’s get through this quick!
1. 2(x + 5)
2. 3 5 − 𝑚
3. 28 1 − 2𝑛
4. 𝑥(𝑥 + 2)
5. 3𝑥 𝑥 − 3
6. 𝑥2(𝑥 − 1)
1. 4𝑦(3𝑦 + 2)
2. 𝑎 2𝑎 − 1
3. −1 7𝑥 + 8
4. ℎ ℎ − 25
Extension:
1. ℎ + 5 ℎ − 5
2. (𝑥 + 3)(𝑥 − 3)

15. Factorise – Part 2
Factorise Completely: 𝑥2+2𝑥 − 15
𝑥 + 5 × (𝑥 − 3)
× ( )
𝑥 × (𝑥 )
𝑥 + × (𝑥− )
Multiply to get -15
-3 and 5
3 and -5
-1 and 15
1 and -15
Add to make 2
-3 and 5
3 and -5
-1 and 15
1 and 15

16. Factorise – Part 2
Factorise Completely: 𝑥2−7𝑥 + 6
𝑥 − 1 × ( 𝑥 − 6 )
× ( )
𝑥 × (𝑥 )
𝑥 − × (𝑥− )
Multiply to get 6
1 and 6
-1 and -6
2 and 3
-2 and -3
Add to make -7
1 and 6
-1 and -6
2 and 3
-2 and -3

17. Exam Questions
Factorise: 8𝑥3 𝑦2 − 4𝑥𝑦3
= 4𝑥2 𝑦2(2𝑥 − 𝑦)
Factorise: 2𝑧2
+ 𝑧
= 𝑧(2𝑧2 + 1)

18. Charades
• http://www.transum.org/Software/Mathswords/Defaul
t.asp