find the perfect square of a^2-6ab-9b^2
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Step-by-step explanation:
a
2
−
6
a
b
+
9
b
2
Rewrite
9
b
2
as
(
3
b
)
2
.
a
2
−
6
a
b
+
(
3
b
)
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
⋅
a
⋅
(
−
3
b
)
Simplify.
2
a
b
=
−
6
a
b
Factor using the perfect square trinomial rule
a
2
−
2
a
b
+
b
2
=
(
a
−
b
)
2
, where
a
=
a
and
b
=
−
3
b
.
(
a
−
3
b
)
2
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