Ex 12.1, 1 (viii) - Chapter 12 Class 8 Factorisation

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Ex 12.1, 1 Find the common factors of the given terms. (viii) 〖3𝑥〗^2 𝑦^3,〖10𝑥〗^3 𝑦^2, 6𝑥^2 𝑦^2 𝑧〖𝟑𝒙〗^𝟐 𝒚^𝟑 = 3 × 𝑥^2 × 𝑦^2 = 2 × 𝒙 × 𝒙 × 𝒚 × 𝒚 × 𝒚 〖𝟏𝟎𝒙〗^𝟑 𝒚^𝟐 = 10 × 𝑥^3 × 𝑦^2 = 2 × 5 × 𝑥^3 × 𝑦^2 = 2 × 5 × 𝒙 × 𝒙 × 𝒙 × 𝒚 × 𝒚 𝟔𝒙^𝟐 𝒚^𝟐 𝒛 = 6 × 𝑥^2 × 𝑦^2 × 𝑧 = 2 × 3 × 𝑥^2 × 𝑦^2 × 𝑧 = 2 × 3 × 𝒙 × 𝒙 × 𝒚 × 𝒚 × 𝒛 So, 〖𝟑𝒙〗^𝟐 𝒚^𝟑 = 3 × 𝑥 × 𝑥 × 𝑦 × 𝑦 × 𝑦 〖𝟏𝟎𝒙〗^𝟑 𝒚^𝟐 = 2 × 5 × 𝑥 × 𝑥 × 𝑥 × 𝑦 × 𝑦 𝟔𝒙^𝟐 𝒚^𝟐 𝒛 = 2 × 3 × 𝑥 × 𝑥 × 𝑦 × 𝑦 × 𝑧 So, Common factor = 𝑥 × 𝑥 × 𝑦 × 𝑦 = (𝑥 × 𝑥) × (𝑦 × 𝑦) = 𝑥^2 × 𝑦^2 = 𝒙^𝟐 𝒚^𝟐