Question

Find the value of (5a -7b) ^3+(9c-5a)^3+(7b-9c)^3

Answer 1

(5a -7b) ^3+(9c-5a)^3+(7b-9c)^3


Using the formula a^3 +b^3+ c^3 = 3abc


(5a -7b) ^3+(9c-5a)^3+(7b-9c)^3 =
3(5a-7b)(9c-5a)(7b-9c)

Answer 2

Answer:

a^3+b^3+c^3-3abc= (a+b+c)(a^2+b^2+c^2-ab-bc-ca)

but since

a+b+c=0

that is

(5a-7b)+(9c-5a)+(7b-9c)=0

a^3+b^3+c^3=0

a^3+b^3+c^3-3abc=0

a^3+b^3+c^3=3abc

=3(5a-7b)(9c-5a)(7b-9c)