Ex 12.2, 3 (iii) - Chapter 12 Class 8 Factorisation

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Ex 12.2, 3 (Method 1) Factorise the expressions. (iii) 2𝑥^3 + 2〖𝑥𝑦〗^2 + 2x𝑧^22𝑥^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 12.2, 3 (Method 2) Factorise the expressions. (iii) 2𝑥^3 + 2〖𝑥𝑦〗^2 + 2x𝑧^2 2𝑥^3 2〖𝑥𝑦〗^2 2x𝑧^2 So, 2 and 𝒙 are the common factors. 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) = 2 × 𝑥 × 𝑥 × 𝑥 = 2 × 𝑥 × 𝑦 × 𝑦 = 2 × 𝑥 × 𝑧 × 𝑧