factorise x^6-26x^3-27
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Step-by-step explanation:
6
−
26
x
3
−
27
Rewrite
x
6
as
(
x
3
)
2
.
(
x
3
)
2
−
26
x
3
−
27
Let
u
=
x
3
. Substitute
u
for all occurrences of
x
3
.
u
2
−
26
u
−
27
Factor
u
2
−
26
u
−
27
using the AC method.
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(
u
−
27
)
(
u
+
1
)
Replace all occurrences of
u
with
x
3
.
(
x
3
−
27
)
(
x
3
+
1
)
Rewrite
27
as
3
3
.
(
x
3
−
3
3
)
(
x
3
+
1
)
Since both terms are perfect cubes, factor using the difference of cubes formula,
a
3
−
b
3
=
(
a
−
b
)
(
a
2
+
a
b
+
b
2
)
where
a
=
x
and
b
=
3
.
(
x
−
3
)
(
x
2
+
x
⋅
3
+
3
2
)
(
x
3
+
1
)
Simplify.
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(
x
−
3
)
(
x
2
+
3
x
+
9
)
(
x
3
+
1
)
Rewrite
1
as
1
3
.
(
x
−
3
)
(
x
2
+
3
x
+
9
)
(
x
3
+
1
3
)
Since both terms are perfect cubes, factor using the sum of cubes formula,
a
3
+
b
3
=
(
a
+
b
)
(
a
2
−
a
b
+
b
2
)
where
a
=
x
and
b
=
1
.
(
x
−
3
)
(
x
2
+
3
x
+
9
)
(
(
x
+
1
)
(
x
2
−
x
⋅
1
+
1
2
)
)
Factor.
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(
x
−
3
)
(
x
2
+
3
x
+
9
)
(
x
+
1
)
(
x
2
−
x
+
1
)
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