This document provides examples of factorizing algebraic expressions by finding the highest common factor (HCF) of the terms. It shows expressions being factorized, such as 2a+6 being written as 2(a+3), and 8m+12 being written as 4(2m+3). The document explains that algebraic expressions can sometimes be written as the HCF multiplied by grouped terms in parentheses. It provides steps for finding the factors of each term and the HCF to factorize expressions like 9jk+4k as k(9j+4).

1. Factorising Algebraic Expressions

2. This is factorising…8 =4×2 =8×1 6𝑎 =6×𝑎 =6𝑎×1 𝑚2 =𝑚×𝑚 12𝑦2 =3×4𝑦2 =4𝑦×3𝑦

3. This is an algebraic expression:2𝑎+6 Algebraic expressions can sometimes be factorised.2×(𝑎+3) = 2𝑎+6 = 2(𝑎+3)

4. 𝑎 𝑎 6 + 2𝑎

5. 𝑎+3 𝑎+3 2×(𝑎+3) 2(𝑎+3) Factorised algebraic expression

6. 2𝑎+6 Factors of 𝟐𝒂 Factors of 𝟔 3, 2, 1, 6 2, 1, 𝑎 𝐻𝐶𝐹=2 =2×𝑎 + 2×3 2𝑎+6 =2×(𝑎+3) =2(𝑎+3)

7. 8𝑚+12 Factors of 𝟖𝒎 Factors of 𝟏𝟐 3, 4, 2, 6, 1, 12 1, 8, 2, 4, 𝑚 𝐻𝐶𝐹=4 + 4×3 =4×2𝑚 8𝑚+12 =4×(2𝑚+3) =4(2𝑚+3)

8. 5𝑎𝑏+10𝑎 Factors of 𝟓𝒂𝒃 Factors of 𝟏𝟎𝒂 2, 5, 1, 10, 𝑎 1, 5, 𝑎, 𝑏 𝐻𝐶𝐹=5𝑎 + 5𝑎×2 =5𝑎×𝑏 5𝑎𝑏+10𝑎 =5𝑎×(𝑏+2) =5𝑎(𝑏+2)

9. 9𝑗𝑘+4𝑘 Factors of 𝟗𝒋𝒌 Factors of 𝟒𝒌 1, 4, 𝑘 1, 9, 𝑗, 𝑘 𝐻𝐶𝐹=𝑘 + 𝑘×4 =𝑘×9𝑗 9𝑗𝑘+4𝑘 =𝑘×(9𝑗+4) =𝑘(9𝑗+4)

10. 𝐻𝐶𝐹=3 12h+3 =3×4h+3×1 + =3(4h+1) 4h 1 𝐻𝐶𝐹=𝑏 𝑎𝑏−4𝑏 =𝑏×𝑎−𝑏×4 =𝑏(𝑎−4) 𝑎 4 −