Is it true that $(102) 3$ can be evaluated using an identity.

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True

False

answer is A.

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Detailed Solution

The given expression is

(102) 3

.
We have to check if the expression can be evaluated.
We must note the following important identity.

a + b ³ = a ³ + b ³ + 3ab (a + b) … (i)

We can substitute the variables a, b, c on the left–hand side of this identity (i) with any values and obtain the expanded form by putting the respective values on the right–hand side of the identity (i).
Now, we have the following observation.
We can find the cubes of numbers greater than 10 or 100 or 1000 or 10000 by expressing them as (10 +a), (100+a), (1000 + a), or (10000 + a); where ‘a’ is any number.
On the other hand, we can also write the numbers less than 10 or 100 or 1000 or 1000 by expressing them as (10–a), (100–a), (1000 – a), or (10000–a); where ‘a’ is any number.
The number

(102) 3

is expanded in the following way using the identity (i).
Substitute 102=100+2 in the identity (i) to get the following expansion after simplification.