Evaluate each of the following:$111^3 – 89^3$

Given:

$111^3 – 89^3$

To do:

We have to evaluate $111^3 – 89^3$.

Solution:

We know that,

$(a+b)^3=a^3 + b^3 + 3ab(a+b)$

$(a-b)^3= a^3-b^3-3ab(a-b)$

This implies,

$a^3 + b^3 = (a + b)^3 - 3ab(a + b)$

$a^3 - b^3 = (a - b)^3 + 3 ab(a - b)$

Therefore,

$111^3 - 89^3 = (111 - 89)^3 + 3 \times 111 \times 89(111 - 89)$

$= (22)^3 + 3 \times 111 \times 89 \times 22$

$= 10648 + 652014$

$= 662662$

Hence, $111^3 - 89^3 = 662662$.

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Updated on: 10-Oct-2022

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