Ex 14.2, 3 (iii) - Factorise 2x^3 + 2xy^2 + 2xz^2

Ex 14.2, 3 (Method 1) Factorise the expressions. (iii) 2𝑥^3 + 2〖𝑥𝑦〗^2 + 2x𝑧^2 2𝑥^3 = 2 × 𝑥^3 = 2 × 𝑥^3 2〖𝑥𝑦〗^2= 2 × 𝑥 × 𝑦^2 = 2 × 𝑥 × 𝑦 × 𝑦 2x𝑧^2 = 2 × 𝑥 × 𝑧^2 = 2 × 𝑥 × 𝑧 × 𝑧 2𝑥^3 + 2〖𝑥𝑦〗^2 + 2x𝑧^2 = (2 × 𝑥 × 𝑥 × 𝑥) + (2 × 𝑥 × 𝑦 × 𝑦) + (2 × 𝑥 × 𝑧 × 𝑧) Taking 2 × 𝑥 Common, = 2 × 𝑥 ((𝑥 × 𝑥) + (y × y) + (z × z)) = 2𝒙 (𝒙^𝟐 + 𝒚^𝟐 + 𝒛^𝟐) Ex 14.2, 3 (Method 2) Factorise the expressions. (iii) 2𝑥^3 + 2〖𝑥𝑦〗^2 + 2x𝑧^2 2𝑥^3 + 2〖𝑥𝑦〗^2 + 2x𝑧^2 = (2 × 𝑥^3) + (2 × 〖𝑥𝑦〗^2) + (2 × 𝑥𝑧^2) Taking 2 common = 2 (𝑥^3 + 〖𝑥𝑦〗^2 + 𝑥𝑧^2) = 2 ((𝑥 × 𝑥^2) + (𝑥 × 𝑦^2) + (𝑥 × 𝑧^2)) Taking 𝑥 common, = 2𝒙 (𝒙^𝟐 + 𝒚^𝟐 + 𝒛^𝟐) 2𝑥^3 + 2〖𝑥𝑦〗^2 + 2x𝑧^2 = (2 × 𝑥^3) + (2 × 〖𝑥𝑦〗^2) + (2 × 𝑥𝑧^2) Taking 2 common = 2 (𝑥^3 + 〖𝑥𝑦〗^2 + 𝑥𝑧^2) = 2 ((𝑥 × 𝑥^2) + (𝑥 × 𝑦^2) + (𝑥 × 𝑧^2)) Taking 𝑥 common, = 2𝒙 (𝒙^𝟐 + 𝒚^𝟐 + 𝒛^𝟐)

Ex 14.2, 3 (iii) - Chapter 14 Class 8 Factorisation