Question

multiply with formula (a²+a+1)(a²-a+1)(a⁴-a²+1)​

Answer 1

Answer:

a⁸+a⁴+1

Step-by-step explanation:

Given that,

(a²+a+1)(a²-a+1)(a⁴-a²+1)

⇒((a²+1)+a)((a²+1)-a)((a⁴+1)-a²

(∵ (a+b)(a-b) = a²-b² )

⇒((a²+1)² - a²)((a⁴+1)-a²)

(∵(a+b²) = a²+b²+2ab ) & (∵(a^m)^n = a^(m×n)

⇒((a⁴+1²+2(a²)(1))-a²)((a⁴+1)-a²)

⇒(a⁴+1+2a²-a²)((a⁴+1)-a²)

⇒(a⁴+1+a²)((a⁴+1)-a²)

⇒((a⁴+1)+a²)((a⁴+1)-a²)

⇒((a⁴+1)²-(a²)²)

⇒(a⁸+1²+2a⁴(1)-a⁴)

⇒(a⁸+1+2a⁴-a⁴)

⇒(a⁸+a⁴+1)

∴(a²+a+1)(a²-a+1)(a⁴-a²+1) = (a⁸+a⁴+1)

HOPE THIS WOULD BE HELPFUL FOR YOU

Answer 2

Answer:

Step-by-step explanation:

Given that,

(a²+a+1)(a²-a+1)(a⁴-a²+1)

⇒((a²+1)+a)((a²+1)-a)((a⁴+1)-a²

(∵ (a+b)(a-b) = a²-b² )

⇒((a²+1)² - a²)((a⁴+1)-a²)

(∵(a+b²) = a²+b²+2ab ) & (∵(a^m)^n = a^(m×n)

⇒((a⁴+1²+2(a²)(1))-a²)((a⁴+1)-a²)

⇒(a⁴+1+2a²-a²)((a⁴+1)-a²)

⇒(a⁴+1+a²)((a⁴+1)-a²)

⇒((a⁴+1)+a²)((a⁴+1)-a²)

⇒((a⁴+1)²-(a²)²)

⇒(a⁸+1²+2a⁴(1)-a⁴)

⇒(a⁸+1+2a⁴-a⁴)

⇒(a⁸+a⁴+1)

∴(a²+a+1)(a²-a+1)(a⁴-a²+1) = (a⁸+a⁴+1)

HOPE THIS WOULD BE HELPFUL FOR YOU