Evaluate each of the following:$46^3 + 34^3$

Given:

$46^3 + 34^3$

To do:

We have to evaluate $46^3 + 34^3$.

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,

$46^3 + 34^3 = (40 + 6)^3 + (40 - 6)^3$

$= 2[(40)^3 + 3 \times 40 \times 62]$

$= 2[64000 + 3 \times 40 \times 36]$

$= 2[64000 + 4320]$

$= 2 \times 68320$

$= 136640$

Hence, $46^3 + 34^3 = 136640$.

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Updated on: 10-Oct-2022

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