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