Question:
Find the value
$8 x^{3}-125 y^{3}+216+180 x y$
Solution:
$=(2 x)^{3}+(-5 y)^{3}+6^{3}-3 \times(2 x)(-5 y)(6)$
$=(2 x+(-5 y)+6)\left((2 x)^{2}+(-5 y)^{2}+6^{2}-2 x \times(-5 y)-(-5 y)^{6}-6(2 x)\right)$
$=(2 x-5 y+6)\left(4 x^{2}+25 y^{2}+36+10 x y+30 y-12 x\right)$
$\therefore 8 x^{3}-125 y^{3}+216+180 x y$
$=(2 x-5 y+6)\left(4 x^{2}+25 y^{2}+36+10 x y+30 y-12 x\right)$
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