Book Online Demo

Check Your IQ

Try Test

Courses

What will be the value of $a − 3 b 3 + 3 b − c 3 + c − a 3$ ?

see full answer

21% of IItians & 23% of AIIMS delhi doctors are from Sri Chaitanya institute !!

An Intiative by Sri Chaitanya

3 (a − 3 b) (3 b − c) (c − a)

4 (a − 3 b) (3 b − c) (c − a)

5 (a − 3 b) (3 b − c) (c − a)

6 (a − 3 b) (3 b − c) (c − a)

answer is A.

(Unlock A.I Detailed Solution for FREE)

Ready to Test Your Skills?

Check your Performance Today with our Free Mock Test used by Toppers!

Take Free Test

Detailed Solution

We have to find the value of

a − 3 b 3 + 3 b − c 3 + c − a 3

.
Using the formula,

x 3 + y 3 + z 3 − 3 x y z = (x + y + z) (x 2 + y 2 + z 2 − x y − y z − z x

)
And, the factorization of the sum of the cubes when their sum is zero, if

x + y + z = 0

then

x 3 + y 3 + z 3 = 3 x y z

.
Let

x = a − 3 b

y = 3 b − c

z = c − a

x 3 + y 3 + z 3 = (x + y + z) (x 2 + y 2 + z 2 − x y − y z − z x)

Calculating

x + y + z

= a − 3 b + 3 b − c + c − a

= 0

Then,
3xyz

= 3 (a − 3 b) (3 b − c) (c − a)

So, the value of

a − 3 b 3 + 3 b − c 3 + c − a 3

3 (a − 3 b) (3 b − c) (c − a)

.
Therefore, option 1 is correct.

Watch 3-min video & get full concept clarity