Evaluate the following: 46^3 + 34^3 - Vidyadip

Question

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

✓

Answer

Given,
$46^3 + 34^3$
The above equation can be written as $(40 + 6)^3 + (40 - 6)^3$
We know that, $(a + b)^3 + (a - b)^3 = 2[a^3 + 3ab^2]$
here, $a = 40, b = 4$
$(40 + 6)^3 + (40 - 6)^3= 2[40^3 + 3(6)^2(40)]$
$= 2[64000 + 4320]$
$= 2[68320]$
$= 1366340$
The value of $46^3 + 34^3 = 1366340$

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