Ex 4.1, 1

Transcript

Ex 4.1, 1 (i) Using the identity (𝑎+𝑏)^2=𝑎^2+2𝑎𝑏+𝑏^2, expand the following (i) (7𝑥+4𝑦)^2 (7𝑥+4𝑦)^2 = (7𝑥)^2+(4𝑦)^2+2(7𝑥)(4𝑦) = 7^2 × 𝑥^2+4^2 × 𝑦^2+(2 × 7 × 4)(𝑥×𝑦) = 𝟒𝟗𝒙^𝟐+𝟏𝟔𝒚^𝟐+𝟓𝟔𝒙𝒚 (𝑎+𝑏)^2=𝑎^2+𝑏^2+2𝑎𝑏 Putting 𝑎 = 7𝑥 & 𝑏 = 4𝑦 Ex 4.1, 1 (ii) Using the identity (𝑎+𝑏)^2=𝑎^2+2𝑎𝑏+𝑏^2, expand the following (ii) (7/5 𝑥+3/2 𝑦)^2 (7/5 𝑥+3/2 𝑦)^2 = (7/5 𝑥)^2+ (3/2 𝑦)^2+2(7/5 𝑥)(3/2 𝑦) = 7^2/5^2 𝑥^2 +3^2/2^2 𝑦^2 + (2 × 7 × 3)/(5 × 2) 𝑥𝑦 = 𝟒𝟗/𝟐𝟓 𝒙^𝟐 +𝟗/𝟒 𝒚^𝟐 + 𝟐𝟏/𝟓 𝒙𝒚 (𝑎+𝑏)^2=𝑎^2+𝑏^2+2𝑎𝑏 Putting 𝑎 = 7/5 𝑥 & 𝑏 = 3/2 𝑦 Ex 4.1, 1 (iii) Using the identity (𝑎+𝑏)^2=𝑎^2+2𝑎𝑏+𝑏^2, expand the following (iii) (2.5𝑝+1.5𝑞)^2 (𝟐.𝟓𝒑+𝟏.𝟓𝒒)^𝟐 = (2.5𝑝)^2+(1.5𝑞)^2+ 2(2.5𝑝)(1.5𝑞) = 〖2.5〗^2 × 𝑝^2+〖1.5〗^2 × 𝑞^2+(2 × 2.5 × 1.5)×(𝑝 × 𝑞) = (25/10)^2 𝑝^2+(15/10)^2 𝑞^2 + (2×25/10×15/10)𝑝𝑞 = 625/100 𝑝^2+225/100 𝑞^2+750/100 𝑝𝑞 = 𝟔.𝟐𝟓𝒑^𝟐+𝟐.𝟐𝟓𝒒^𝟐+𝟕.𝟓𝒑𝒒 (𝑎+𝑏)^2=𝑎^2+𝑏^2+2𝑎𝑏 Putting 𝑎 = 2.5𝑝 & 𝑏 = 1.5𝑞 Ex 4.1, 1 (iv) Using the identity (𝑎+𝑏)^2=𝑎^2+2𝑎𝑏+𝑏^2, expand the following (iv) (3/4 𝑠+8𝑡)^2 (3/4 𝑠+8𝑡)^2 = (3/4 𝑠)^2+ (8𝑡)^2+2(3/4 𝑥)(8𝑡) = 3^2/4^2 𝑠^2 +8^2 𝑡^2 + (2 × 3 × 8)/4 𝑠𝑡 = 𝟗/𝟏𝟔 𝒔^𝟐 +𝟔𝟒𝒕^𝟐 +𝟏𝟐𝒔𝒕 (𝑎+𝑏)^2=𝑎^2+𝑏^2+2𝑎𝑏 Putting 𝑎 = 3/4 𝑠 & 𝑏 = 8𝑡 Ex 4.1, 1 (v) Using the identity (𝑎+𝑏)^2=𝑎^2+2𝑎𝑏+𝑏^2, expand the following (v) (𝑥+1/2𝑦)^2 (𝑥+1/2𝑦)^2 = (𝑥)^2+ (1/2𝑦)^2+2(𝑥)(1/2𝑦) = 𝑥^2 +1/(2^2 × 𝑦^2 ) +2/2 × 𝑥/𝑦 = 𝒙^𝟐 +𝟏/(𝟒𝒚^𝟐 ) +𝒙/𝒚 (𝑎+𝑏)^2=𝑎^2+𝑏^2+2𝑎𝑏 Putting 𝑎 = 𝑥 & 𝑏 = 1/2𝑦 Ex 4.1, 1 (vi) Using the identity (𝑎+𝑏)^2=𝑎^2+2𝑎𝑏+𝑏^2, expand the following (vi) (1/𝑥+1/𝑦)^2 (1/𝑥+1/𝑦)^2 = (1/𝑥)^2+ (1/𝑦)^2+2(1/𝑥)(1/𝑦) = 1/𝑥^2 +1/𝑦^2 +2/(𝑥 × 𝑦) = 𝟏/𝒙^𝟐 +𝟏/𝒚^𝟐 +𝟐/𝒙𝒚 (𝑎+𝑏)^2=𝑎^2+𝑏^2+2𝑎𝑏 Putting 𝑎 = 1/𝑥 & 𝑏 = 1/𝑦