Question

Factorise: 8x^3-125y^3​

Answer 1

8
x
3
−
125
y
3
8
x
3
-
125
y
3
Rewrite
8
x
3
8
x
3
as
(
2
x
)
3
(
2
x
)
3
.
(
2
x
)
3
−
125
y
3
(
2
x
)
3
-
125
y
3
Rewrite
125
y
3
125
y
3
as
(
5
y
)
3
(
5
y
)
3
.
(
2
x
)
3
−
(
5
y
)
3
(
2
x
)
3
-
(
5
y
)
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
)
a
3
-
b
3
=
(
a
-
b
)
(
a
2
+
a
b
+
b
2
)
where
a
=
2
x
a
=
2
x
and
b
=
5
y
b
=
5
y
.
(
2
x
−
(
5
y
)
)
(
(
2
x
)
2
+
2
x
(
5
y
)
+
(
5
y
)
2
)
(
2
x
-
(
5
y
)
)
(
(
2
x
)
2
+
2
x
(
5
y
)
+
(
5
y
)
2
)
(
2
x
−
5
y
)
(
4
x
2
+
10
x
y
+
25
y
2
)