We first find a square + b square + c square by expanding (a + b + c) square, which equals 5. Substituting these evaluated numerical components into the standard three-variable cubic identity gives minus 25.
If a + b + c = 5 and ab + bc + ca = 10, then prove that a cube + b cube + c cube – 3abc = -25.
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We utilize the algebraic identity for a three-variable cube expression. The identity states that the target expression equals (a + b + c) multiplied by the quantity (a square + b square + c square – ab – bc – ca). We first square the addition equation to get 25 = (a square + b square + c square) + 2(10), meaning the squared sum equals 5. Plugging these values back into our main identity yields 5 times (5 – 10), which equals minus 25.
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/