x^8+x^4+1 how to solve this equation
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Answer:
Step-by-step explanation:Rewrite the middle term.
x
8
+
(
2
x
4
⋅
1
−
x
4
)
+
1
Rearrange terms.
x
8
+
2
x
4
⋅
1
+
1
−
x
4
Factor first three terms by perfect square rule.
(
x
4
+
1
)
2
−
x
4
Rewrite
x
4
as
(
x
2
)
2
.
(
x
4
+
1
)
2
−
(
x
2
)
2
Since both terms are perfect squares, factor using the difference of squares formula,
a
2
−
b
2
=
(
a
+
b
)
(
a
−
b
)
where
a
=
x
4
+
1
and
b
=
x
2
.
(
x
4
+
1
+
x
2
)
(
x
4
+
1
−
x
2
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