Question

If a+b+c=0 , then find the value of ..... (-2a)^3 + (-2b)^3 + (-2c)^3 - 3 (-2a)(-2b)(-2c)............. plzzzz answer me fast I will mark your answer as brainlist​

Answer 1

Answer:

0

Step-by-step explanation:

Given Equation is (-2a)³ + (-2b)³ + (-2c)³ - 3(-2a)(-2b)(-2c)

Now,

∴ a³ + b³ + c³ - 3abc = (a + b + c)(a² + b² + c² - ab - bc - ca)

⇒ (-2a)³ + (-2b)³ + (-2c)³ - 3(-2a)(-2b)(-2c) = (0)[a² + b² + c² - ab - bc - ca]

⇒ (-2a)³ + (-2b)³ + (-2c)³ = 0.

Hope it helps!

Answer 2

We are given an expression that a + b + c = 0 , we know that when such a case occurs a³ + b³ + c³ = 3 abc . When we have to find (-2 a)³ + (-2 b)³ + (-2 c)³ - 3 (-2 a)(-2 b)(-2 c ) , we will have to multiply both sides by - 2 first and then proceed .

Given :

a + b + c = 0

Multiply both sides by -2 :

⇒ - 2 ( a + b + c ) = 0

⇒ - 2 a - 2 b - 2 c = 0

Transpose 2 c to the other side :

⇒ - 2 a - 2 b = 2 c

Cube both sides :

Using ( a + b )³ = a³ + b³ + 3 ab ( a + b )

⇒ - 8 a³ - 8 b³ - 3 ( - 2 a )( - 2 b ) ( -2 a - 2 b ) = ( 2 c )³

We know that ( -2 a - 2 b ) = 2 c

⇒ ( -2 a )³ + ( - 2 b)³ + ( - 2 c )³ - 3 ( - 2 a )( - 2 b )( - 2 c ) = 0

The value of the expression will be 0 .