A slideshow to explain the process of factorising algebraic expressions.

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 −