Factorize: 81m^4 - (n-m)^4
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81
m
4
−
1
Rewrite
81
m
4
as
(
9
m
2
)
2
.
(
9
m
2
)
2
−
1
Rewrite
1
as
1
2
.
(
9
m
2
)
2
−
1
2
Since both terms are perfect squares, factor using the difference of squares formula,
a
2
−
b
2
=
(
a
+
b
)
(
a
−
b
)
where
a
=
9
m
2
and
b
=
1
.
(
9
m
2
+
1
)
(
9
m
2
−
1
)
Simplify.
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(
9
m
2
+
1
)
(
3
m
+
1
)
(
3
m
−
1
)
([)]|√>≥π
789
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