expand:
(a+b)^3-(a-b)^3
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Answer:
Use the Binomial expansion (note the exponents sum to the power in each term):
(
x
+
y
)
3
=
3
C
0
x
3
y
0
+
3
C
1
x
2
y
1
+
3
C
2
x
1
y
2
+
3
C
3
x
0
y
3
Remember
3
!
=
3
⋅
2
⋅
1
=
6
,
2
!
=
2
⋅
1
=
2
,
1
!
=
1
and
0
!
=
1
_
3
C
0
=
3
!
(
3
−
0
)
!
(
0
!
)
=
3
!
(
3
)
!
1
=
1
_
3
C
1
=
3
!
(
3
−
1
)
!
(
1
!
)
=
3
!
(
2
)
!
1
=
3
⋅
2
!
2
!
=
3
_
3
C
2
=
3
!
(
3
−
2
)
!
(
2
!
)
=
3
!
(
1
)
!
2
!
=
3
⋅
2
!
2
!
=
3
_
3
C
3
=
3
!
(
3
−
3
)
!
(
3
!
)
=
3
!
0
!
⋅
3
!
=
1
Note:
(
a
−
b
)
3
=
(
a
+
(
−
b
)
)
3
Substitute into the Binomial expansion formula,
let
x
=
a
and
y
=
−
b
:
(
a
−
b
)
3
=
a
3
+
3
a
2
(
−
b
)
1
+
3
a
(
−
b
)
2
+
(
−
b
)
3
=
a
3
−
3
a
2
b
+
3
a
b
2
−
b
3
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