write down the expansion of (1-x)^3
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Algebra Examples
Popular Problems Algebra Expand using the Binomial Theorem (1-x)^3
(
1
−
x
)
3
Use the binomial expansion theorem to find each term. The binomial theorem states
(
a
+
b
)
n
=
n
∑
k
=
0
n
C
k
⋅
(
a
n
−
k
b
k
)
.
3
∑
k
=
0
3
!
(
3
−
k
)
!
k
!
⋅
(
1
)
3
−
k
⋅
(
−
x
)
k
Expand the summation.
3
!
(
3
−
0
)
!
0
!
⋅
(
1
)
3
−
0
⋅
(
−
x
)
0
+
3
!
(
3
−
1
)
!
1
!
⋅
(
1
)
3
−
1
⋅
(
−
x
)
+
3
!
(
3
−
2
)
!
2
!
⋅
(
1
)
3
−
2
⋅
(
−
x
)
2
+
3
!
(
3
−
3
)
!
3
!
⋅
(
1
)
3
−
3
⋅
(
−
x
)
3
Simplify the exponents for each term of the expansion.
1
⋅
(
1
)
3
⋅
(
−
x
)
0
+
3
⋅
(
1
)
2
⋅
(
−
x
)
+
3
⋅
(
1
)
⋅
(
−
x
)
2
+
1
⋅
(
1
)
0
⋅
(
−
x
)
3
Simplify each term.
Step-by-step explanation:
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