
Example 1 Factorise 12π^2b + 15γππγ^2 12a^2b + 15ab^2 12a^2b = 12 Γ a^2b = 2 Γ 2 Γ 3 Γ a^2b = 2 Γ 2 Γ 3 Γ a Γ a Γ b 15ab^2 = 15 Γ ab^2 = 3 Γ 5 Γ ab^2 = 3 Γ 5 Γ a Γ b Γ b Now, 12ab^2 = 2 Γ 2 Γ 3 Γ a Γ a Γ b 15ab^2 = 3 Γ 5 Γ a Γ b Γ b So, 3, a, b are common factors. 12ab^2 + 15ab^2 = 2 Γ 2 Γ 3 Γ a Γ a Γ b + 3 Γ 5 Γ a Γ b Γ b = 3 Γ a Γ b (2 Γ 2 Γ a + 5 Γ b) = 3ab (4a + 5b)