Find the value
Question:

Find the value

$a^{3}+3 a^{2} b+3 a b^{2}+b^{3}-8$

Solution:

$=(a+b)^{3}-8$

$\left[\therefore a^{3}+3 a^{2} b+3 a b^{2}+b^{3}=(a+b)^{3}\right]$

$=(a+b)^{3}-23$

$=(a+b-2)\left((a+b)^{2}+(a+b) \times 2+2^{2}\right)$

$=(a+b-2)\left(a^{2}+2 a b+b^{2}+2 a+2 b+4\right)$

$\therefore a^{3}+3 a^{2} b+3 a b^{2}+b^{3}-8=(a+b-2)\left(a^{2}+2 a b+b^{2}+2 a+2 b+4\right)$

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