What is the factored form of 8x^24-27y^6 someone please help me please
1 answer:
Answer:
x
24
−
27
y
6
Rewrite
8
x
24
as
(
2
x
8
)
3
.
(
2
x
8
)
3
−
27
y
6
Rewrite
27
y
6
as
(
3
y
2
)
3
.
(
2
x
8
)
3
−
(
3
y
2
)
3
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
=
2
x
8
and
b
=
3
y
2
.
(
2
x
8
−
(
3
y
2
)
)
(
(
2
x
8
)
2
+
2
x
8
(
3
y
2
)
+
(
3
y
2
)
2
)
Simplify.
Tap for more steps...
(
2
x
8
−
3
y
2
)
(
4
x
16
+
6
x
8
y
2
+
9
y
4
)
x
24
−
27
y
6
Rewrite
8
x
24
as
(
2
x
8
)
3
.
(
2
x
8
)
3
−
27
y
6
Rewrite
27
y
6
as
(
3
y
2
)
3
.
(
2
x
8
)
3
−
(
3
y
2
)
3
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
=
2
x
8
and
b
=
3
y
2
.
(
2
x
8
−
(
3
y
2
)
)
(
(
2
x
8
)
2
+
2
x
8
(
3
y
2
)
+
(
3
y
2
)
2
)
Simplify.
Tap for more steps...
(
2
x
8
−
3
y
2
)
(
4
x
16
+
6
x
8
y
2
+
9
y
4
)
Explanation:
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