Question

(b+c)^3 (b-c)^3 + (c-a)^3 (c+a)^3+(a+b)^3(a-b)^3

Answer 1

Step-by-step explanation:

Hello!!

Here is your answer

Given

$((b + c)(b - c)) {}^{3} + ((c + a)(c - a)) {}^{3} + ((a + b)(a - b)) {}^{3} = (b {}^{2} - c {}^{2} ) {}^{3} + (c {}^{2} - a {}^{2} ) {}^{3} + (a {}^{2} - b {}^{2} ) {}^{3}$

as x+y+z = 0

x^3+y^3+z^3 = 3xyz

So answer is

$3(b {}^{2} - c {}^{2} )(c {}^{2} - a {}^{2} )(a {}^{2} - b {}^{2} )$