Question

Evaluate: a2 (b2 – c2) + b2 (c2 – a2) + c2 (a2 – b2)​

Answer 1

Answer:

0

Step-by-step explanation:

a2b2 - a2c2 + b2c2 -a2b2 +c2a2 - b2c2

every term will cancel it's counter part with opposite sign and we will get 0

Answer 2

Lets do

$\\ \sf\longmapsto {a}^{2} ( {b}^{2} - {c}^{2} ) + {b}^{2} ( {c}^{2} - {a}^{2} )+ {c}^{2} ( {a}^{2} - {b}^{2} ) \\ \\ \sf\longmapsto {a}^{2} {b}^{2} - {a}^{2} {c}^{2} + {b}^{2} {c}^{2} - {b}^{2} {a}^{2} + {c}^{2} {a}^{2} - {c}^{2} {b}^{2} \\ \\ \sf\longmapsto {a}^{2} {b}^{2} - {a}^{2} {c}^{2} + {b}^{2} {c}^{2} - {a}^{2} {b}^{2} + {a}^{2} {c}^{2} - {b}^{2} {c}^{2} \\ \\ \sf \longmapsto \: { a}^{2} {b}^{2} - {a}^{2} {b}^{2} + {b}^{2} {c}^{2} - {b}^{2} {c}^{2} + {a}^{2} {c}^{2} - {a}^{2} {c}^{2} \\ \\ \sf \longmapsto \: 0 + 0 + 0 \\ \\ \sf \longmapsto \: 0$