Evaluate each of the following:$93^3 – 107^3$

Given:

$93^3 – 107^3$

To do:

We have to evaluate $93^3 – 107^3$.

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,

$(a + b)^3 + (a- b)^3 = 2(a^3 + 3ab^2)$

$(a + b)^3 - (a - b)^3 = 2(b^3 + 3a^2b)$

Therefore,

$93^3 - 107^3 = -[(107)^3 - (93)^3]$

$= -[(100 + 7)^3 - (100 - 7)^3]$

$= -2[(7)^3 + 3(100)^2 \times 7]$

$= -2(343 + 3 \times 10000 \times 7]$

$= -2[343 + 210000]$

$= -2[210343]$

$= -420686$

Hence, $93^3 - 107^3 = -420686$. 

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Updated on: 10-Oct-2022

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