We express 117 as 100 + 10 + 7 and apply the three-term identity. Squaring each number and adding all the double-product combinations yields the correct numerical total.
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To calculate the square of 117 efficiently, we split the number into three manageable parts: 100 + 10 + 7. This allows us to use the algebraic identity for a three-term addition square, where a equals 100, b equals 10, and c equals 7. We find the squares of these numbers, which are 10000, 100, and 49. Adding these to the cross-product terms 2000, 1400, and 140 results in 13689.
For more NCERT Solutions for Class 9 Maths Ganita Manjari Chapter 4 Exploring Algebraic Identities (2026-27):
https://www.tiwariacademy.com/ncert-solutions/class-9/maths/ganita-manjari-chapter-4/