Question

evaluate (103) whole cube by using suitable identity

Answer 1

(103)³ = (100 + 3)³

(a + b)³ = a³ + b³ + 3 x a² × b + 3 x a x b³
           = 100³ + 3 ³ + 3 ×100² × 3 + 3 × 100 × 3²
             = 100000 + 27 + 90000 + 2700
                  = 1092727

Answer 2

Given:

(103) whole cube.

To find:

The value of (103) whole cube.

Solution:

To answer this question, first of all, we should know about one of the algebraic identities which is

${(a + b)}^{3} = {a}^{3} + {b}^{3} + 3 {a}^{2} b + 3a {b}^{2}$

Now, proceeding to the solution,

As we know that 103 can be written as the sum of 100 and 3.

So,

${(103)}^{3} = {(100 + 3)}^{3}$

By using the above algebraic identity, we have,

${(100 + 3)}^{3} = {(100)}^{3} + {(3)}^{3} + (3){100}^{2} (3) + (3)(100) {(3)}^{2}$

On solving the above, we get

$= 1000000 + 27 + 90000 + 2700$

$= 1092727$

Hence, the whole cube of 103 is equal to 10,92,727.