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Pattern 1
Last updated at January 13, 2026 by Teachoo
Class 8 (Ganita Prakash - 1, 2 & Old NCERT)
Chapter 6 Class 8 - We Distribute yet things Multiply (Ganita Prakash)
- Distributive Property
- Figure it out - Page 142, 143
- Fast Multiplications Using the Distributive Property
- Square of the Sum/Difference of Two Numbers
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Investigating Patterns
- Figure it out - Page 149
- Mind the Mistake, Mend the Mistake
- This Way or That Way, All Ways Lead to the Bay
- Area of Shaded Region
- Figure it out - Page 154-156
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)
