Solve the following
16p - 40mn +25n² =?
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16
m
2
−
40
m
n
+
25
n
2
Rewrite
16
m
2
as
(
4
m
)
2
.
(
4
m
)
2
−
40
m
n
+
25
n
2
Rewrite
25
n
2
as
(
5
n
)
2
.
(
4
m
)
2
−
40
m
n
+
(
5
n
)
2
Check that the middle term is two times the product of the numbers being squared in the first term and third term.
40
m
n
=
2
⋅
(
4
m
)
⋅
(
5
n
)
Rewrite the polynomial.
(
4
m
)
2
−
2
⋅
(
4
m
)
⋅
(
5
n
)
+
(
5
n
)
2
Factor using the perfect square trinomial rule
a
2
−
2
a
b
+
b
2
=
(
a
−
b
)
2
, where
a
=
4
m
and
b
=
5
n
.
(
4
m
−
5
n
)
2
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