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Factorize each of the following expressions:
$1029 -3x^3$
Given:
$1029 -3x^3$
To do:
We have to factorize the given expression.
Solution:
We know that,
$a^3 + b^3 = (a + b) (a^2 - ab + b^2)$
$a^3 - b^3 = (a - b) (a^2 + ab + b^2)$
Therefore,
$1029 - 3x^3 = 3(343 - x^3)$
$= 3[(7)^3 - (x)^3]$
$= 3(7 - x)[(7)^2+7\times x+(x)^2]$
$= 3(7 - x) (49x + 7x + x^2)$
Hence, $1029 - 3x^3 = 3(7 - x) (49x + 7x + x^2)$.
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