Question
Evaluate the following:
$93^3 - 107^3$
$93^3 - 107^3$
✓
Answer
Given,
$93^3-107^3$
the above equation can be written as $(100-7)^3-(100+7)^3$
we know that, $(a-b)^3-(a+b)^3=-2\left[b^3+3 b a^2\right]$
here, $a=93, b=107$
$(100-7)^3-(100+7)^3=-2\left[7^3+3(100)^2(7)\right]$
$=-2[343+210000]$
$=-2[210343]$
$=-420686$
The value of $93^3-107^3=-420686$
$93^3-107^3$
the above equation can be written as $(100-7)^3-(100+7)^3$
we know that, $(a-b)^3-(a+b)^3=-2\left[b^3+3 b a^2\right]$
here, $a=93, b=107$
$(100-7)^3-(100+7)^3=-2\left[7^3+3(100)^2(7)\right]$
$=-2[343+210000]$
$=-2[210343]$
$=-420686$
The value of $93^3-107^3=-420686$
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