Question
Factorise:
$8-27 b^3-343 c^3-126 b c$
$8-27 b^3-343 c^3-126 b c$
✓
Answer
$8-27 b^3-343 c^3-126 b c$
$=(2)^3+(-3 b)^3+(-7 c)^3-3 \times(2) \times(-3 b) \times(-7 c)$
$=\left[2+(-3 b)+(-7 c)\left[(2)^2+(-3 b)^2+(-7 c)^2-(2)(-3 b)-(-3 b)(-7 c)-(2)(-7 c)\right]\right.$
$=(2-3 b-7 c)\left(4+9 b^2+49 c^2+6 b-21 b c+14 c\right)$
$=(2)^3+(-3 b)^3+(-7 c)^3-3 \times(2) \times(-3 b) \times(-7 c)$
$=\left[2+(-3 b)+(-7 c)\left[(2)^2+(-3 b)^2+(-7 c)^2-(2)(-3 b)-(-3 b)(-7 c)-(2)(-7 c)\right]\right.$
$=(2-3 b-7 c)\left(4+9 b^2+49 c^2+6 b-21 b c+14 c\right)$
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