factor(x+1)^4 -(x-1)^4
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Answer:
x
2
+
x
+
1
4
Rewrite
1
as
1
2
.
x
2
+
x
+
1
2
4
Rewrite
4
as
2
2
.
x
2
+
x
+
1
2
2
2
Rewrite
1
2
2
2
as
(
1
2
)
2
.
x
2
+
x
+
(
1
2
)
2
Check the middle term by multiplying
2
a
b
and compare this result with the middle term in the original expression.
2
a
b
=
2
⋅
x
⋅
1
2
Simplify.
2
a
b
=
x
Factor using the perfect square trinomial rule
a
2
+
2
a
b
+
b
2
=
(
a
+
b
)
2
, where
a
=
x
and
b
=
1
2
.
(
x
+
1
2
)
2
Step-by-step explanation:
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