Factorise (x+3)^3-2(x+3)^2+3(x+3)
Answers
Answered by
26
Both terms are cubes and the expression can be factored as:
a
3
+
b
3
=
(
a
+
b
)
(
a
2
−
a
b
+
b
2
)
To make the process easier to follow,
let
(
x
−
3
)
=
m
and
(
3
x
−
2
)
=
n
m
3
+
n
3
=
(
m
+
n
)
(
m
2
−
m
n
+
n
2
)
=
(
x
−
3
+
3
x
−
2
)
(
(
x
−
3
)
2
−
(
x
−
3
)
(
3
x
−
2
)
+
(
3
x
−
2
)
2
)
Simplify:
=
(
4
x
−
5
)
(
x
2
−
6
x
+
9
−
(
3
x
2
−
11
x
+
6
)
+
9
x
2
−
12
x
+
4
)
=
(
4
x
−
5
)
(
x
2
−
6
x
+
9
−
3
x
2
+
11
x
−
6
+
9
x
2
−
12
x
+
4
)
=
(
4
x
−
5
)
(
7
x
2
−
7
x
+
7
)
=
7
(
4
x
−
5
)
(
x
2
−
x
+
1
)
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