Write down the product of (x² + x + 1) ( x² - x + 1) and ( x⁴- x² + 1)
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Answer:
(a
3
−b
3
)=a
3
−a
2
b+a
2
b−ab
2
+ab
2
−b
3
=(a
3
−a
2
b)+(a
2
b−ab
2
)+(ab
2
−b
3
)
=a
2
(a−b)+ab(a−b)+b
2
(a−b)
=(a−b)(a
2
+ab+b
2
)
Now, given (x
2
−1)(x
4
+x
2
+1)
=(x
2
−1)((x
2
)
2
+x
2
(1)+1
2
)
=((x
2
)
3
−1
3
)
=x
6
−1
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