Question
Evaluate the following : $111^3 - 89^3$
✓
Answer
Given,
$111^3 - 89^3$
the above equation can be written as $(100 + 11)^3 - (100 - 11)^3$
we know that, $(a + b)^3 - (a - b)^3 = 2[b^3 + 3ab^2]$
here,$ a = 100 b = 11$
$(100 + 11)^3 - (100 - 11)^{3 }= 2[11^3 + 3(100)^2(11)]$
$= 2[1331 + 330000]$
$= 2[331331]$
$= 662662$
The value of $111^3 - 89^3 $
$= 662662$
$111^3 - 89^3$
the above equation can be written as $(100 + 11)^3 - (100 - 11)^3$
we know that, $(a + b)^3 - (a - b)^3 = 2[b^3 + 3ab^2]$
here,$ a = 100 b = 11$
$(100 + 11)^3 - (100 - 11)^{3 }= 2[11^3 + 3(100)^2(11)]$
$= 2[1331 + 330000]$
$= 2[331331]$
$= 662662$
The value of $111^3 - 89^3 $
$= 662662$
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