factorizes :(ax+by)²+(bx-ay)²
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Given : (ax+by)
2
+(bx−ay)
2
By using the formula (a+b)
2
and(a−b)
2
'we get,
=a
2
x
2
+b
2
y
2
+2abxy+b
2
x
2
+a
2
y
2
−2abxy
=a
2
x
2
+b
2
y
2
+b
2
x
2
+a
2
y
2
Rearranging the terms
=a
2
x
2
+b
2
x
2
+b
2
y
2
+a
2
y
2
By taking the common terms out
=x
2
(a
2
+b
2
)+y
2
(a
2
+b
2
)
So we get,
(ax+by)
2
+(bx−ay)
2
= (a
2
+b
2
)(x
2
+y
2
)
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