Question 1 - Think & Reflect Box 1 (Page 79) - Factorisation Using Algebra Tiles - Chapter 4 Class 9 - Exploring Algebraic Identities (Ganita Manjari I)

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Question 1 - Think & Reflect Box 1 (Page 79) Suppose 7𝑥 is split as 2𝑥+5𝑥; can a similar rectangular arrangement be formed? Consider other possibilities and check. This question is talking about factorization of x2 + 7x + 12 using this figure Here, 7x is split as 4x + 3x And, we ae asked is 7x can be split as 2x + 5x Now, To form a perfect rectangle, the tiny unit tiles in the corner must form a perfect grid If we put 2𝑥 tiles on the side and 5𝑥 tiles on the bottom, the empty space in the corner would require 𝟐×𝟓=𝟏𝟎 unit tiles to fill perfectly But our equation gives us 12 unit tiles We would have 2 leftover tiles sticking out, meaning it's not a perfect rectangle Thus, we cannot split 7x into 2x and 5x Rule of thumb The two numbers you split the middle term into MUST multiply to give you the constant (last) number This is what we will use in Splitting the Middle term Method