Question

simplify
(a²-b²)³+(b²-c²)³+(c²-a²)³/(a-b)³+(b-c)³+(c-a)³​

Answer 1

Step-by-step explanation:

mark me as brainliest...

plzzzzzz

.

Answer 2

AnswEr:

We have,

$\tt \: ( {a}^{2} - {b}^{2} ) + ( {b}^{2} - {c}^{2} ) + ( {c}^{2} - {a}^{2} ) = 0 \\ \\ \therefore \: \tt \: ( {a}^{2} - {b}^{2} ) {}^{3} + ( {b}^{2} - {c}^{2} ) {}^{3} +( {c}^{2} - {a}^{2} ) {}^{3} \\ \tt = 3( {a}^{2} - {b}^{2} )( {b}^{2} - {c}^{2} )( {c}^{2} - {a}^{2} ) \\ \\ \implies \tt \: ( {a}^{2} - {b}^{2} ) {}^{3} + ( {b}^{2} - {c}^{2} ) {}^{3} +( {c}^{2} - {a}^{2} ) {}^{3} \\ \tt \: = 3(a - b)(a + b)(b - c)(b + c) \\ \tt \: (c - a)(c +a)$

___________________________________

Similarly, we have,

$\tt \: (a - b) + (b - c) + (c - a) = 0 \\ \\ \implies \tt \: (a - b) {}^{3} + (b - c) {}^{3} + (c - a) {}^{3} \\ \tt \: = 3(a - b)(b + c)(c - a) \\ \\ \therefore \tt \frac{( {a}^{2} - {b}^{2}) {}^{3} + ( {b}^{2} - {c}^{2}) {}^{3}( {c}^{2} - {a}^{2}) {}^{3} }{(a - b) {}^{3} + (b - c) {}^{3} + (c - a) {}^{3} } \\ \\ = \tt \: \frac{3(a - b)(a + b)(b - c)(b + c)(c - a)(c + a)}{3(a - b)(b - c)(c - a)} \\ = \tt \: (a + b)(b + c)(c + a)$