Answer:
To factorize
x
9
−
1
, we can use the identity
a
3
−
b
3
=
(
a
−
b
)
(
a
2
+
a
b
+
b
2
)
.
Hence
x
9
−
1
=
(
x
3
)
3
−
1
3
=
(
x
3
−
1
)
(
x
6
+
x
3
+
1
)
factorizing
x
3
−
1
further
x
9
−
1
=
(
x
3
−
1
)
(
x
6
+
x
3
+
1
)
=
(
x
−
1
)
(
x
2
+
x
+
1
)
(
x
6
+
x
3
+
1
)