Question:
Find the value
$125+8 x^{3}-27 y^{3}+90 x y$
Solution:
$=(5)^{3}+(2 x)^{3}+(-3 y)^{3}-3 \times 5 \times 2 x \times(-3 y)$
$=(5+2 x+(-3 y))\left(5^{2}+(2 x)^{2}+(-3 y)^{2}-5(2 x)-2 x(-3 y)-(-3 y) 5\right)$
$=(5+2 x-3 y)\left(25+4 x^{2}+9 y^{2}-10 x+6 x y+15 y\right)$
$\therefore 125+8 x^{3}-27 y^{3}+90 x y$
$=(5+2 x-3 y)\left(25+4 x^{2}+9 y^{2}-10 x+6 x y+15 y\right)$
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