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

Last updated at Dec. 16, 2024 by

Ex 9.5, 4 - Chapter 9 Class 8 Algebraic Expressions and Identities - Part 6

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Question 4 Simplify. (iv) (4𝑚+5𝑛)^2+(5𝑚+4𝑛)^2 Solving (𝟒𝒎+𝟓𝒏)^𝟐 (𝑎+𝑏)^2=𝑎^2+𝑏^2+2𝑎𝑏 Putting 𝑎 = 4𝑚 & 𝑏 = 5𝑛 = (4𝑚)^2+(5𝑛)^2+2(4𝑚)(5𝑛) = 16𝑚^2+25𝑛^2+40𝑚𝑛 Solving (𝟓𝒎+𝟒𝒏)^𝟐 (𝑎+𝑏)^2=𝑎^2+𝑏^2+2𝑎𝑏 Putting 𝑎 = 5𝑚 & 𝑏 = 4𝑛 = (5𝑚)^2+(4𝑛)^2+2(5𝑚)(4𝑛) = 25𝑚^2+16𝑛^2+40𝑚𝑛 ∴ (4𝑚+5𝑛)^2+(5𝑚+4𝑛)^2 = (16𝑚^2+25𝑛^2+40𝑚𝑛)+(25𝑚^2+16𝑛^2+40𝑚𝑛) = (16𝑚^2+25𝑚^2 )+(25𝑛^2+16𝑛^2 )+(40𝑚𝑛+40𝑚𝑛) = 𝟒𝟏𝒎^𝟐+𝟒𝟏𝒏^𝟐+𝟖𝟎𝒎𝒏

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Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 14 years. He provides courses for Maths, Science and Computer Science at Teachoo