Resolve into facters : 27X³ - 64
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Answer:
When factorising the sum of cubes, we use the formula
a
3
+
b
3
=
(
a
+
b
)
(
a
2
−
a
b
+
b
2
)
.
In this case of
27
x
3
+
64
,
27
x
3
=
a
3
64
=
b
3
Find
a
:
27
x
3
=
a
3
3
√
27
x
3
=
3
√
a
3
3
x
=
a
Find
b
:
64
=
b
3
3
√
64
=
3
√
b
3
4
=
b
Substitute
a
=
3
x
and
b
=
4
into
(
a
+
b
)
(
a
2
−
a
b
+
b
2
)
(
3
x
+
4
)
(
(
3
x
)
2
−
(
3
x
×
4
)
+
4
2
)
=
(
3
x
+
4
)
(
9
x
2
−
12
x
+
16
)
(
3
x
+
4
)
(
9
x
2
−
12
x
+
16
)
is the factorised form of
27
x
3
+
64
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