Question

factorise :25x⁴-60x²y²+36y⁴​

Answer 1

Rewrite
25
x
2
25
x
2
as
(
5
x
)
2
(
5
x
)
2
.
(
5
x
)
2
−
60
x
y
+
36
y
2
(
5
x
)
2
-
60
x
y
+
36
y
2
Rewrite
36
y
2
36
y
2
as
(
6
y
)
2
(
6
y
)
2
.
(
5
x
)
2
−
60
x
y
+
(
6
y
)
2
(
5
x
)
2
-
60
x
y
+
(
6
y
)
2
Check the middle term by multiplying
2
a
b
2
a
b
and compare this result with the middle term in the original expression.
2
a
b
=
2
⋅
(
5
x
)
⋅
(
−
6
y
)
2
a
b
=
2
⋅
(
5
x
)
⋅
(
-
6
y
)
Simplify.
2
a
b
=
−
60
x
y
2
a
b
=
-
60
x
y
Factor using the perfect square trinomial rule
a
2
−
2
a
b
+
b
2
=
(
a
−
b
)
2
a
2
-
2
a
b
+
b
2
=
(
a
-
b
)
2
, where
a
=
5
x
a
=
5
x
and
b
=
−
6
y
b
=
-
6
y
.
(
5
x
−
6
y
)
2