Pattern 1

Last updated at July 23, 2026 by

Pattern 1 - Chapter 6 Class 8 Ganita Prakash Part 1 [Teachoo] - Investigating Patterns

part 2 - Pattern 1 - Investigating Patterns - Chapter 6 Class 8 - We Distribute yet things Multiply (Ganita Prakash) - Class 8 (Ganita Prakash - 1, 2 & Old NCERT)

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Transcript

Pattern 1Look at the following pattern. 2 (22 + 12) = 32 + 12 2 (32 + 12) = 42 + 22 2 (62 + 52) = 112 + 12 2 (52 + 32) = 82 + 22 Basically, this pattern is 2 × (a2 + b2) = (a + b)2 + (a – b)2 Lets look at how we can prove this (a + b)2 = a2 + b2 + 2ab (a – b)2 = a2 + b2 – 2ab Adding both equations (a + b)2 + (a – b)2 = (a2 + b2 + 2ab) + (a2 + b2 – 2ab) (a + b)2 + (a – b)2 = a2 + a2 + b2 + b2 + 2ab – 2ab) (a + b)2 + (a – b)2 = 2a2 + 2b2 (a + b)2 + (a – b)2 = 2 × (a2 + b2)

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