set [tex] (8d^{6} j^{3})^{3} [/tex] = x
and [tex](3 s^{10} t^{5} )^{3} [/tex] = y
therefore: x³ + y³
= (x+y)(x²-xy+y²)
= [ (8d^6 j^3) + (3s^10 t^5) ] [ (8d^6 j^3)² + (8d^6 j^3)(3s^10 t^5) + (3s^10 t^5)² ]
= [ (2d²j)³ +(3s^10 t^5) ] [ (2d²j)^6 + (2d²j)³(3s^10 t^5) + (3s^10 t^5)² ]
729-b^6c^12
= 9³-(b²c^4)³
=[9 - (b²c^4)] [81+81(b²c^4)+(b²c^4)²]
=[ 3² - (bc²)² ] [81+81(b²c^4)+(b²c^4)²]
=[ 3 + (bc²)] [ 3 - (bc²) ] [81+81(b²c^4)+(b²c^4)²]
