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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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