Question

By using suitable identities, evaluate the following:
(i) (103)^3
(i) (99)^3​​

Answer 1

Answer:

1. 1092727

2. 970299

Step-by-step explanation:

use

( a-b) whole cube formuale

Answer 2

$\huge{\underline{\underline{\tt{ Solution : }}}}$

1) $\tt{ {(103)}^{3}}$ can be written as : $\tt{ {(100+3)}^{3}}$

If we carefully observe ; $\tt{ {100+3}^{3}}$ is in the form of $\tt{ {(a+b)}^{3}}$ so we will use the same identity to solve the given problem.

a = 100

b = 3

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

When we substitute the values of (a) and (b) we get :

$\longrightarrow{\tt{ {(a+b)}^{3} = {100}^{3} + {3}^{3} + 3 \times{100}^{2}\times 3 + 3 \times 100 \times{3}^{2}}}$

$\longrightarrow{\tt{ 1000000 + 27 + 3 \times 10000 \times 3 + 300 \times 9}}$

$\implies{\tt{ 1092727}}$

Answer : $\large{\boxed{\tt{ 1092727}}}$

Verification :

$\tt{ \sqrt[3] {1092727} \implies 103}$

__________________

2)$\tt{ {99}^{3}}$ can be written as $\tt{ {(100-1)}^{3}}$

If we carefully observe the given problem is in the form of $\tt{ {(a-b)}^{3}}$ . So ,we will use the same identity to solve the given problem.

a = 100

b = 1

$\tt{ {(a-b)}^{3} = {a}^{3} - {b}^{3} - 3\times {a}^{2}\times b + 3 \times a \times {b}^{2}}$

When we substitute the values of (a) and (b) we get :

$\longrightarrow{\tt{ {(a-b)}^{3} = {100}^{3} - {1}^{3} - 3 \times {100}^{2} \times 1 + 3 \times 100 times {1}^{2}}}$

$\longrightarrow{\tt{ 1000000 - 1 - 3 \times 10000 \times 1 + 300 \times 1}}$

$\implies{\tt{ 970299}}$

Answer : $\large{\boxed{\tt{970299}}}$

Verification :

$\tt{\sqrt[3]{970299} \implies 99}$