This six-term polynomial matches the expanded three-term identity. The squared bases are m/3, k/2, and 3n, which merge into the single grouped factor (m/3 + k/2 + 3n) square.
Factor using suitable identities: m square/9 + mk/3 + k square/4 + 3nk + 2mn + 9n square
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We observe that this long expression has six separate terms, which indicates it comes from a three-term square identity. The three perfect square terms are m square/9, k square/4 and 9n square, which are the squares of m/3, k/2 and 3n respectively. The remaining three terms perfectly match the double cross-products of these bases. Therefore, the complete factored form is (m/3 + k/2 + 3n) square.
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/