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Example 10 - Simplify (a + b) (2a - 3b + c) - (2a - 3b)c - Class 8

Example 10 - Chapter 9 Class 8 Algebraic Expressions and Identities - Part 2

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Example 10 Simplify (a + b) (2a – 3b + c) – (2a – 3b) c. Here there are two expressions 1st expression = (𝑎+𝑏) (2𝑎−3𝑏+𝑐) 2nd expression = (2𝑎−3𝑏) 𝑐 Solving 1st expression (𝑎+𝑏) (2𝑎−3𝑏+𝑐) = 𝑎(2𝑎−3𝑏+𝑐)+𝑏(2𝑎−3𝑏+𝑐) = (𝑎×2𝑎)−(𝑎×3𝑏)+(𝑎×𝑐)+(𝑏×2𝑎)−(𝑏×3𝑏)+(𝑏×𝑐) = 2𝑎^2−3𝑎𝑏+𝑎𝑐+2𝑎𝑏−3𝑏^2+𝑏𝑐 = 2𝑎^2−3𝑏^2+𝑎𝑐+𝑏𝑐−3𝑎𝑏 +2𝑎𝑏 = 2𝑎^2−3𝑏^2+𝑎𝑐+𝑏𝑐−𝑎𝑏 Solving 2nd expression (2𝑎−3𝑏)𝑐 = 2𝑎𝑐−3𝑏𝑐 Now, our expression is (𝑎+𝑏)(2𝑎−3𝑏+𝑐)−(2𝑎−3𝑏)𝑐 = 2𝑎^2−3𝑏^2+𝑎𝑐+𝑏𝑐−𝑎𝑏−(2𝑎𝑐−3𝑏𝑐) = 2𝑎^2−3𝑏^2+𝑎𝑐+𝑏𝑐−𝑎𝑏−2𝑎𝑐+3𝑏𝑐 = 2𝑎^2−3𝑏^2−𝑎𝑏+(𝑎𝑐−2𝑎𝑐)+(𝑏𝑐+3𝑏𝑐) = 𝟐𝒂^𝟐−𝟑𝒃^𝟐−𝒂𝒃−𝒂𝒄+𝟒𝒃𝒄

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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.