Question

(y^4-y^2+1)(y^4+y^2+1)=y^8+y^4+1

Answer 1

Ответ:

(y^4+1) ^2-y^4=y^8+y^4+1

y^8+2y^4+1-y^4=y^8+y^4+1

2y^4-y^4=y^4

y^4=y^4

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Answer 2

To prove that (y^4 - y^2 + 1)(y^4 + y^2 + 1) is equal to y^8 + y^4 + 1, we can expand the left-hand side of the equation and simplify:

Starting with (y^4 - y^2 + 1)(y^4 + y^2 + 1):

= y^4(y^4 + y^2 + 1) - y^2(y^4 + y^2 + 1) + (y^4 + y^2 + 1) = y^8 + y^6 + y^4 - y^6 - y^4 - y^2 + y^4 + y^2 + 1 = y^8 + y^4 + 1

Therefore, (y^4 - y^2 + 1)(y^4 + y^2 + 1) is indeed equal to y^8 + y^4 + 1.