math factorize

a⁶k⁶ - 1
= (a³k³)² - 1
= (a³k³ + 1)(a³k³ - 1) <--- Recall formula: x² - y² = (x+y)(x-y)
= [(ak)³ + 1][(ak)³ - 1]
= (ak+1)[(ak)²-ak+1][(ak)³ - 1] <--- Recall formula: x³ + y³ = (x+y)(x²-xy+y²)
= (ak+1)[(ak)²-ak+1](ak-1)[(ak)²+ak+1] <--- Recall formula: x³ - y³ = (x-y)(x²-+xy+y²)

= (ak+1)(ak-1)(a²k²+ak+1)(a²k²-ak+1)