Ex 8.2

Chapter 8 Class 8 Algebraic Expressions and Identities
Serial order wise                   This video is only available for Teachoo black users This video is only available for Teachoo black users This video is only available for Teachoo black users This video is only available for Teachoo black users This video is only available for Teachoo black users This video is only available for Teachoo black users This video is only available for Teachoo black users

Learn in your speed, with individual attention - Teachoo Maths 1-on-1 Class

### Transcript

Ex 8.2, 3 Complete the table of products.For 2x 2𝑥 × −5𝑦 = 2 × 𝑥 × −5 × 𝑦 = (2 × −5) × 𝑥 × 𝑦 = −10 × 𝑥 × 𝑦 = −10𝑥𝑦 𝟐𝒙 × 𝟑𝒙^𝟐 = 2 × 𝑥 × 3 × 𝑥^2 = (2 × 3) × (𝑥 × 𝑥^2 ) = 6 × 𝑥^3 = 𝟔𝒙^𝟑 𝟐𝒙 × −𝟒𝒙𝒚 = 2 × 𝑥 × −4 × 𝑥 × y = (2 × −4) × (𝑥 × 𝑥) × 𝑦 = −8 ×〖 𝑥〗^2 × 𝑦 = −𝟖𝒙^𝟐 𝒚 𝟐𝒙 × 𝟕𝒙^𝟐 𝒚 = 2 × 𝑥 × 7 × 𝑥^2 × y = (2 × 7) × (𝑥 × 𝑥^2 ) × 𝑦 = 14 × 𝑥^3 × 𝑦 = 𝟏𝟒𝒙^𝟑 𝒚 𝟐𝒙 × −𝟗𝒙^𝟐 𝒚^𝟐 = 2 × 𝑥 × −9 × 𝑥^2 × y^2 = (2 × −9) × (𝑥 × 𝑥^2 ) × 𝑦^2 = −18 × 𝑥^3 × 𝑦^2 = −𝟏𝟖𝒙^𝟑 𝒚^𝟐 Thus, our table looks like (−𝟓𝒚) × (−𝟓𝒚) = −5 × 𝑦 × −5 × 𝑦 = (−5 × −5) × (𝑦 × 𝑦) = 25 × 𝑦^2 = 𝟐𝟓𝒚^𝟐 (−𝟓𝒚) × (−𝟒𝒙𝒚) = −5 × 𝑦 × −4 × 𝑥 × 𝑦 = (−5 × −4) × 𝑦 × 𝑦 × 𝑥 = 20 × 𝑦^2 × 𝑥 = 𝟐𝟎𝒚^𝟐 𝒙 For −5y (−𝟓𝒚) × 𝟕𝒙^𝟐 𝒚 = −5 × 𝑦 × 7 × 𝑥^2 × 𝑦 = (−5 × 7) × (𝑦 × 𝑦) × 𝑥^2 = −35 × 𝑦^2 × 𝑥^2 = −𝟑𝟓𝒚^𝟐 𝒙^𝟐 (−𝟓𝒚) × (−𝟗𝒙^𝟐 𝒚^𝟐 ) = −5 × 𝑦 × (−9) × 𝑥^2 × 𝑦^2 = (−5 × −9) × 𝑥^2 × (𝑦 × 𝑦^2 ) = 45 × 𝑥^2 × 𝑦^3 = 𝟒𝟓𝒙^𝟐 𝒚^𝟑 Thus, our table looks like For 3x2 𝟑𝒙^𝟐 × 𝟑𝒙^𝟐 = 3 × 𝑥^2 × 3 × 𝑥^2 = (3 × 3) × (𝑥^2 × 𝑥^2 ) = 9 × 𝑥^4 = 𝟗𝒙^𝟒 𝟑𝒙^𝟐 × (−𝟒𝒙𝒚) = 3 × 𝑥^2 × −4 × 𝑥 × 𝑦 = (3 × −4) × (𝑥^2 × 𝑥) × 𝑦 = −12 × 𝑥^3 × 𝑦 = −𝟏𝟐𝒙^𝟑 𝒚 For 3x2 𝟑𝒙^𝟐 × 𝟑𝒙^𝟐 = 3 × 𝑥^2 × 3 × 𝑥^2 = (3 × 3) × (𝑥^2 × 𝑥^2 ) = 9 × 𝑥^4 = 𝟗𝒙^𝟒 𝟑𝒙^𝟐 × (−𝟒𝒙𝒚) = 3 × 𝑥^2 × −4 × 𝑥 × 𝑦 = (3 × −4) × (𝑥^2 × 𝑥) × 𝑦 = −12 × 𝑥^3 × 𝑦 = −𝟏𝟐𝒙^𝟑 𝒚 𝟑𝒙^𝟐 × 𝟕𝒙^𝟐 𝒚 = 3 × 𝑥^2 × 7 × 𝑥^2 × 𝑦 = (3 × 7)×(𝑥^2 × 𝑥^2 ) × 𝑦 = 21 × 𝑥^4 × 𝑦 = 𝟐𝟏𝒙^𝟒 𝒚 𝟑𝒙^𝟐 × (−𝟗𝒙^𝟐 𝒚^𝟐) = 3 × 𝑥^2 × 7 × 𝑥^2 × 𝑦 = (3 × −9) × (𝑥^2 × 𝑥^2 ) × 𝑦^2 = −27 × 𝑥^4 ×𝑦^2 = −𝟐𝟕𝒙^𝟒 𝒚^𝟐 Thus, our table looks like For −4xy (−𝟒𝒙𝒚) × (−𝟒𝒙𝒚) = −4 × 𝑥 × 𝑦 × −4 × 𝑥 × 𝑦 = (−4 × −4) × (𝑥 × 𝑥) × (𝑦 × 𝑦) = 16 × 𝑥^2 × 𝑦^2 = 𝟏𝟔𝒙^𝟐 𝒚^𝟐 (−𝟒𝒙𝒚) × 𝟕𝒙^𝟐 𝒚 = −4 × 𝑥 × 𝑦 × 7 × 𝑥^2 × 𝑦 = (−4 × 7) × (𝑥 × 𝑥^2 ) × (𝑦 × 𝑦) = −28 × 𝑥^3 × 𝑦^2 = −𝟐𝟖𝒙^𝟑 𝒚^𝟐 For −4xy (−𝟒𝒙𝒚) × (−𝟗𝒙^𝟐 𝒚^𝟐 ) = −4 × 𝑥 × 𝑦 × −9 × 𝑥^2 × 𝑦^2 = (−4 × −9) × (𝑥 × 𝑥^2 ) × (𝑦 × 𝑦^2 ) = 36 × 𝑥^3 × 𝑦^3 = 𝟑𝟔𝒙^𝟑 𝒚^𝟑 Thus, our table looks like (𝟕𝒙^𝟐 𝒚) × (𝟕𝒙^𝟐 𝒚) = 7 × 𝑥^2 × 𝑦 × 7 × 𝑥^2 × 𝑦 = (7 × 7) × (𝑥^2 × 𝑥^2 ) × (𝑦 × 𝑦) = 49 × 𝑥^4 × 𝑦^2 = 𝟒𝟗𝒙^𝟒 𝒚^𝟐 (𝟕𝒙^𝟐 𝒚) × (−𝟗𝒙^𝟐 𝒚^𝟐 ) = 7 × 𝑥^2 × 𝑦 × −9 × 𝑥^2 × 𝑦^2 = (7 × −9) × (𝑥^2 × 𝑥^2 ) × (𝑦 × 𝑦^2 ) = −63 × 𝑥^4 × 𝑦^3 = −𝟔𝟑𝒙^𝟒 𝒚^𝟑 (−𝟗𝒙^𝟐 𝒚^𝟐 ) × (−𝟗𝒙^𝟐 𝒚^𝟐 ) = −9 × 𝑥^2 × 𝑦^2 × −9 × 𝑥^2 × 𝑦^2 = (−9 × −9) × (𝑥^2 × 𝑥^2 ) × (𝑦^2 × 𝑦^2 ) = 81 × 𝑥^4 × 𝑦^4 = 𝟖𝟏𝒙^𝟒 𝒚^𝟒 