Question

Factorize: (a/b)^3 + (b/c)^3 + (c/a)^3 - 3 using suitable identity

Answer 1

Answer:

=(a/b+b/c+c/a){a²/b²+b²/c²+c²/a²-a/c-b/a-c/b}

Step-by-step explanation:

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

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

=(a/b+b/c+c/a){(a/b)²+(b/c)²+(c/a)²-(a/b)(b/c)-(b/c)(c/a)-(a/b)(c/a)}

=(a/b+b/c+c/a){a²/b²+b²/c²+c²/a²-a/c-b/a-c/b}