We split the middle coefficient minus 1 into minus 7 and positive 6 because their sum equals minus 1 and their product equals minus 42, giving the linear binomial factors.
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To factor this expression without tiles, we apply the middle term splitting method. We need two numbers that add up to minus 1 and multiply to minus 42. These target integers are minus 7 and positive 6. Rewriting the expression gives r square – 7r + 6r – 42. Factoring by grouping in pairs gives r(r – 7) + 6(r – 7). Taking out the common binomial bracket leaves the final factors (r – 7)(r + 6).
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/