Question

factorization : 8x3 - y3 +1+6xy​

Answer 1

$8x³-y³+1+6xy$

$=(2x)³+(-y)³+(1)³-3×2x×(-y)×1$

$=[2x+(-y)+1] \; [(2x)²+(-y)²+(1)²$$- 2x×(-y) - (-y)×1 - 1×2x]$

$= (2x-y+1) (4x²+y²+1+2xy+y-2x)$

$\large \bold {Identity \; Used}$

$a³+b³+c³-3abc = (a+b+c)(a²+b²+c²-ab-bc-ca)$