Ex 4.3, 3

Transcript

Ex 4.3, 3 (i) Expand the following using the identity (𝑎+𝑏+𝑐)^2=𝑎^2+𝑏^2+𝑐^2+2𝑎𝑏+2𝑏𝑐+2𝑐𝑎:. (i) (𝑝+3𝑞+7𝑟)^2 (𝒑+𝟑𝒒+𝟕𝒓)^𝟐 = 𝑝^2+(3q)^2+〖(7𝑟)〗^2 + 2 × 𝑝 ×(3𝑞) + 2 × 𝑝 × (7𝑟)+2 ×(3𝑞) × (7𝑟) = 𝒑^𝟐+𝟗𝒒^𝟐+𝟒𝟗𝒓^𝟐+𝟔𝒑𝒒+𝟏𝟒𝒑𝒓+𝟒𝟐𝒒𝒓 Using (𝑎+𝑏+𝑐)^2=𝑎^2+𝑏^2+𝑐^2+2𝑎𝑏+2𝑏𝑐+2𝑎𝑐 Putting 𝑎 = 𝑝, 𝑏 = 3q & 𝑐 = 7𝑟 Ex 4.3, 3 (ii) Expand the following using the identity (𝑎+𝑏+𝑐)^2=𝑎^2+𝑏^2+𝑐^2+2𝑎𝑏+2𝑏𝑐+2𝑐𝑎:. (ii) (3𝑥−2𝑦+4𝑧)^2 (𝟑𝒙−𝟐𝒚+𝟒𝒛)^𝟐 = 〖(3𝑥)〗^2+(−2y)^2+〖(4𝑧)〗^2 + 2 × (3𝑥) ×(−2𝑦) + 2 × (3𝑥) × (4𝑧)+2 ×(−2𝑦) × (4𝑧) = 〖𝟗𝒙〗^𝟐+𝟒𝒚^𝟐+𝟏𝟔𝒛^𝟐−𝟏𝟐𝒙𝒚+𝟐𝟒𝒙𝒛−𝟏𝟔𝒚𝒛 Using (𝑎+𝑏+𝑐)^2=𝑎^2+𝑏^2+𝑐^2+2𝑎𝑏+2𝑏𝑐+2𝑎𝑐 Putting 𝑎 = 3𝑥, 𝑏 = −2𝑦 & 𝑐 = 4𝑧