Byju's Answer
Standard VIII
Mathematics
Factorisation by Regrouping Terms
Factorise by ...
Question
Factorise by grouping method:
(
a
x
+
b
y
)
2
+
(
b
x
−
a
y
)
2
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Solution
(
a
x
+
b
y
)
2
+
(
b
x
−
a
y
)
2
=
[
(
a
x
)
2
+
(
b
y
)
2
+
(
2
×
a
x
×
b
y
)
]
+
[
(
b
x
)
2
+
(
a
y
)
2
−
(
2
×
b
x
×
a
y
)
]
Using the identities
(
a
+
b
)
2
=
(
a
2
+
b
2
+
2
a
b
)
,
and
(
a
−
b
)
2
=
(
a
2
+
b
2
−
2
a
b
)
]
=
a
2
x
2
+
b
2
y
2
+
2
a
b
x
y
+
b
2
x
2
+
a
2
y
2
−
2
a
b
x
y
=
a
2
x
2
+
b
2
x
2
+
b
2
y
2
+
a
2
y
2
=
x
2
(
a
2
+
b
2
)
+
y
2
(
a
2
+
b
2
)
=
(
a
2
+
b
2
)
(
x
2
+
y
2
)
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