factorise 8x^3-36x^2+54x-19
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Answer:
Notice that
8
x
3
=
(
2
x
)
3
and
−
27
=
(
−
3
)
3
, so is the answer
(
2
x
−
3
)
3
?
Multiply out
(
2
x
−
3
)
3
and find that it is.
8
x
3
−
36
x
2
+
54
x
−
27
=
(
2
x
−
3
)
3
Explanation:
In general,
(
a
+
b
)
3
=
a
3
+
3
a
2
b
+
3
a
b
2
+
b
3
Putting
a
=
2
x
and
b
=
−
3
we find:
(
2
x
−
3
)
3
=
(
2
x
)
3
+
3
(
2
x
)
2
(
−
3
)
+
3
(
2
x
)
(
−
3
)
2
+
(
−
3
)
3
=
8
x
3
−
36
x
2
+
54
x
−
27
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