We separate 205 into 200 + 5 and use the addition square identity. Calculating the squares of both numbers and adding their double cross-product gives the final evaluation.
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To find the value using an algebraic shortcut, we rewrite 205 as the sum of 200 and 5. This lets us use the regular binomial identity where a equals 200 and b equals 5. The square of 200 is 40000 and the square of 5 is 25. The intermediate term is two times 200 times 5, which equals 2000. Adding 40000, 2000 and 25 together gives 42025.
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/