factorise ,8x^3+under root27y^3?
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8
x
3
+
y
3
is a sum of two cubes as it is equivalent to
(
2
x
)
3
+
y
3
Recall the identity
a
3
+
b
3
=
(
a
+
b
)
(
a
2
−
a
b
+
b
2
)
Hence,
8
x
3
+
y
3
=
(
2
x
)
3
+
y
3
=
(
2
x
+
y
)
(
(
2
x
)
2
−
(
2
x
)
y
+
y
2
)
=
(
2
x
+
y
)
(
4
x
2
−
2
x
y
+
y
2
)
Alternatively,
8
x
3
+
y
3
=
8
x
3
+
4
x
2
y
−
4
x
2
y
−
2
x
y
2
+
2
x
y
2
+
y
3
=
4
x
2
(
2
x
+
y
)
−
2
x
y
(
2
x
+
y
)
+
y
2
(
2
x
+
y
)
=
(
2
x
+
y
)
(
4
x
2
−
2
x
y
+
y
2
)
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