Question 4 (iii) - Algebra Identities and Formulas - Chapter 8 Class 8 Algebraic Expressions and Identities

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Ex 9.5, 4 - Chapter 9 Class 8 Algebraic Expressions and Identities - Part 4

Ex 9.5, 4 - Chapter 9 Class 8 Algebraic Expressions and Identities - Part 5

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Question 4 Simplify. (iii) (7𝑚−8𝑛)^2+(7𝑚+8𝑛)^2 Solving (𝟕𝒎−𝟖𝒏)^𝟐 (𝑎−𝑏)^2=𝑎^2+𝑏^2−2𝑎𝑏 Putting 𝑎 = 7𝑚 & 𝑏 = 8𝑛 = (7𝑚)^2+(8𝑛)^2−2(7𝑚)(8𝑛) = 49𝑚^2+64𝑛^2−(14×8)𝑚𝑛 = 49𝑚^2+64𝑛^2−112𝑚𝑛 Solving (𝟕𝒎+𝟖𝒏)^𝟐 (𝑎+𝑏)^2=𝑎^2+𝑏^2+2𝑎𝑏 Putting 𝑎 = 7𝑚 & 𝑏 = 8𝑛 = (7𝑚)^2+(8𝑛)^2+2(7𝑚)(8𝑛) = 49𝑚^2+64𝑛^2+(14×8)𝑚𝑛 = 49𝑚^2+64𝑛^2+112𝑚𝑛 ∴ (7𝑚−8𝑛)^2+(7𝑚+8𝑛)^2 = (49𝑚^2+64𝑛^2−112𝑚𝑛)+(49𝑚^2+64𝑛^2+112𝑚𝑛) = (49𝑚^2+49𝑚^2 )+(64𝑛^2+64𝑛^2 )+(−112𝑚𝑛+112𝑚𝑛) = 𝟗𝟖𝒎^𝟐+𝟏𝟐𝟖𝒏^𝟐

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