Question

8. Show that 2a² +2b² +2c² - 2ab - 2bc
- 2ca = (a - b)² + (b - c)² + (c - a)²​

Answer 1

Step-by-step explanation:

$2a^{2}+2b^{2}+2c^{2}-2ab-2bc-2ca\\=a^{2}+a^{2}+b^{2}+b^{2}+c^{2}+c^{2}-2ab-2bc-2ca\\= a^{2}-2ab+b^{2}+b^{2}-2bc+c^{2}+c^{2}-2ac+a^{2}\\=(a-b)^{2}+(b-c)^{2}+(c-a)^{2}\:(Proved)$

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