1. Day 3: Expanding and Common Factoring
Unit 4: Algebra of Quadratics

2. Learning Goals To be able to expand brackets
To be able to common factor

3. Expanding Brackets
a) 3(𝑥−7)
b) 2𝑥(4𝑥−3)

4. Expanding Brackets Blitz
Fastest to correctly complete the first column wins a prize!

5. Expanding Binomials (𝑥+𝑠)(𝑥+𝑡)
Multiply both of the terms in the first binomial by each of the terms in the second binomial
F irst
O utside
I nside
L ast
Simplify the expression by collecting the like terms

6. Examples
1) (𝑥 + 2)(𝑥 + 3)
2) (𝑎 + 5)(𝑎 – 4)

7. Identifying Factors & Finding Greatest Common Factor
You have15 minutes!

8. Common Factoring The opposite of expanding Expanding: 5 𝑥−2 =5𝑥−10
Find the greatest common factor of all terms

9. State the GCF of each pair.
a) 6 𝑎 3 𝑎𝑛𝑑 9𝑎 What is the GCF for 6 and 9? What is the GCF for 𝑎 3 and 𝑎?

10. State the GCF of each pair.
b) −2 𝑥 4 𝑦 4 𝑎𝑛𝑑 8 𝑥 3 𝑦 5 What is the GCF for −2 and 8? What is the GCF for 𝑥 4 and 𝑥 3 ? What is the GCF for 𝑦 4 and 𝑦 5 ?

11. Factor fully.
a) 7 𝑥 2 −14𝑥+21
b) 6 𝑑 3 +3 𝑑 2 −18𝑑

12. How to Factor:
Find the highest number that divides evenly into the number of each term
For each letter common to every term, use the lowest exponent
Divide each term by the number found in step 1
Subtract the exponent in each term (for each letter) from the exponent found in step 2

13. Factor fully.
c) 4 𝑘 4 −12 𝑘 2 +8𝑘
d) 3 𝑥−1 +4𝑦(𝑥−1)

14. Factor fully.
e) 5𝑚𝑦−𝑡𝑚+5𝑛𝑦+𝑡𝑛

15. Success Criteria
I CAN expand brackets
I CAN find the common factor

16. To Do… Finish earlier worksheets Worksheet
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