Question

Solve (102)³ without actually calculating​

Answer 1

Answer:

1,061,208

Step-by-step Explanation:

$(102 {)}^{3}$

Breaking down 102 into 100 + 2.

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

[Using Identity a³ + b³ + 3ab (a + b)]

$(100 {)}^{3} + (2 {)}^{3} + 3(100 \times 2 \: ) \: \: (100 + 2)$

Add 100 + 2.

$(100 {)}^{3} + {(2)}^{3} + 3(100 \times 2) \: (102)$

Now Multiply (100 × 2) and then multiply the result by 3.

$(100 {)}^{3} + {(2)}^{3} + 3(200)(102)$

${(100)}^{3} + {(2)}^{3} +( 3 \times 200)(102)$

${(100)}^{3} + {(2)}^{3} + 600(102)$

Now, Multiply 100, 3 times as well as 2.

$1000000 + 8 + 600(102)$

Now, Multiply 600 by 102.

$1000000 + 8 + (600 \times 102)$

$1000000 + 8 + 61200$

Now, Add 1,000,000 by 8 and then add result by 61200.

$1000008 + 61200$

$1061208$

Therefore, The answer to (102)³ is 1,061,208.

Verifying:

$(102 {)}^{3}$

Multiply 102, 3 times.

$102 \times 102 \times 102$

$1061208$

Hence, Verified!