Question

if a+2b+c=0 then show that a3+8b3+c3=6abc​

Answer 1

Step-by-step explanation:

given a+2b+c=0

(a + 2b + c)³ = 0

=> (a + 2b)³ + 3(a + 2b)²c + 3(a + 2b)c² + c³=0

=> (a³ + 6a²b + 12ab² + 8b³) + 3c(a + 2b)(a + 2b + c) + c³= 0

= (a³ + 8b³ + c³) + 6ab(a + 2b) = 0

=> a³ + 8b³ + c³ - 6abc = 0

a+2b = -c (given)

=> a³ + 8b³ + c³ = 6abc

Answer 2

Answer:

a + 2b + c = 0

a + 2b = - c

(a + 2b)³ = (-c)³

a³ + 8b³ + 3(a*2b) (a+2b) = -c³

a³ + 8b³ + 6ab(-c) = -c³

a³ + 8b³ - 6abc = -c³

a³ + 8b³ + c³ = 6abc

Hence proved

Expansion:

An algebraic expression multiplied by itself ( any Number of times) when expressed as a polynomial is called an Expansion.

In fact the term 'expansion' is used for the process of such multiplication.

A corollary is a result or relation that follows from another result or relation that is known.