Factorize:
Question:

Factorize:

$8-27 b^{3}-343 c^{3}-126 b c$

 

Solution:

$8-27 b^{3}-343 c^{3}-126 b c=(2)^{3}+(-3 b)^{3}+(-7 c)^{3}-3 \times(2) \times(-3 b) \times(-7 c)$

$=[2+(-3 b)+(-7 c)]\left[(2)^{2}+(-3 b)^{2}+(-7 c)^{2}-(2)(-3 b)-(-3 b)(-7 c)-(2)(-7 c)\right]$

$=(2-3 b-7 c)\left(4+9 b^{2}+49 c^{2}+6 b-21 b c+14 c\right)$

 

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