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Ex 9.4, 3 (iv) - Simplify (a + b) (c - d) + (a - b) (c+d) + 2 (ac+bd)

Ex 9.4, 3 (iv) - Chapter 9 Class 8 Algebraic Expressions and Identities - Part 2
Ex 9.4, 3 (iv) - Chapter 9 Class 8 Algebraic Expressions and Identities - Part 3

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Transcript

Ex 9.4, 3 Simplify. (iv) (𝑎+𝑏) (𝑐−𝑑)+(𝑎−𝑏) (𝑐+𝑑)+2 (𝑎𝑐+𝑏𝑑) Here, there are 3 expressions 1st expression = (𝑎+𝑏) (𝑐−𝑑) 2nd expression = (𝑎−𝑏) (𝑐+𝑑) 3rd expression = 2 (𝑎𝑐+𝑏𝑑) Solving 1st expression (𝑎+𝑏) (𝑐−𝑑) = 𝑎(𝑐−𝑑)+𝑏 (𝑐−𝑑) = (𝑎×𝑐)−(𝑎×𝑑)+(𝑏×𝑐)−(𝑏×𝑑) = 𝑎𝑐−𝑎𝑑+𝑏𝑐−𝑏𝑑 Solving 2nd expression (𝑎−𝑏) (𝑐+𝑑) = 𝑎(𝑐+𝑑)−𝑏 (𝑐+𝑑) = (𝑎×𝑐)+(𝑎×𝑑)−(𝑏×𝑐)−(𝑏−𝑑) = 𝑎𝑐+𝑎𝑑−𝑏𝑐−𝑏𝑑 Solving 3rd expression 2 (𝑎𝑐+𝑏𝑑) = (2×𝑎𝑐)+(2×𝑏𝑑) = 2𝑎𝑐+2𝑏𝑑 Now, our expression becomes (𝑎+𝑏) (𝑐−𝑑)+(𝑎−𝑏) (𝑐+𝑑)+2 (𝑎𝑐+𝑏𝑑) = 𝑎𝑐−𝑎𝑑+𝑏𝑐−𝑏𝑑+𝑎𝑐+𝑎𝑑−𝑏𝑐−𝑏𝑑+2𝑎𝑐+2𝑏𝑑 = (𝑎𝑐+𝑎𝑐+2𝑎𝑐)+(−𝑎𝑑+𝑎𝑑)+(𝑏𝑐−𝑏𝑐)+(−𝑏𝑑−𝑏𝑑+2𝑏𝑑) = (1+1+2)𝑎𝑐+(−1+1)𝑎𝑑+(1−1)𝑏𝑐+(−1−1+2)𝑏𝑑 = 4𝑎𝑐+(0)𝑎𝑑+(0)𝑏𝑐+(0)𝑏𝑑 = 𝟒𝒂𝒄

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Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 13 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.