Question 4 (iv) - 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 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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