Question

x^6-1.Please help me. I will mark as brainliest.​

Answer 1

Answer: (x+1)(x-1)(x²+x+1)(x²-x+1)

Step-by-step explanation:

x⁶-1 = (x³)² - 1²

=(x³+1)(x³-1)

We know that (a-b)³=a³-b³-3ab(a-b)

so a³-b³=(a-b)³+3ab(a-b)

=(a-b)[(a-b)²+3ab

=(a-b)(a²+ab+b²)

Similarly (a+b)³=a³+b³+3ab(a+b)

so a³+b³=(a+b)³-3ab(a+b)

=(a+b)[(a+b)²-3ab

=(a+b)(a²-ab+b²)

∴x⁶-1 =(x³+1)(x³-1)

=(x+1)(x²-x+1)(x-1)(x²+x+1)

=(x+1)(x-1)(x²+x+1)(x²-x+1)

Answer 2

Answer:

(x+1)(x-1)(x²+x+1)(x²-x+1)