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Standard VIII
Mathematics
Properties of Square Numbers
Question
Prove the followings,
i)
(
a
+
b
)
2
+
(
a
−
b
)
2
=
2
(
a
2
+
b
2
)
ii)
(
a
+
b
)
2
−
(
a
−
b
)
2
=
4
a
b
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Solution
Verified by Toppr
We have,
i)
(
a
+
b
)
2
+
(
a
−
b
)
2
=
(
a
2
+
2
a
b
+
b
2
)
+
(
a
2
−
2
a
b
+
b
2
)
=
2
(
a
2
+
b
2
)
ii)
(
a
+
b
)
2
−
(
a
−
b
)
2
=
(
a
2
+
2
a
b
+
b
2
)
−
(
a
2
−
2
a
b
+
b
2
)
=
a
2
+
2
a
b
+
b
2
−
a
2
+
2
a
b
−
b
2
=
4
a
b
.
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5
Similar Questions
Q1
Prove the followings,
i)
(
a
+
b
)
2
+
(
a
−
b
)
2
=
2
(
a
2
+
b
2
)
ii)
(
a
+
b
)
2
−
(
a
−
b
)
2
=
4
a
b
View Solution
Q2
Prove that:
(
a
+
b
)
2
+
(
a
−
b
)
2
=
2
(
a
2
+
b
2
)
.
View Solution
Q3
Prove that:
(
a
+
b
)
2
−
(
a
−
b
)
2
=
4
a
b
View Solution
Q4
Question 33
The value of
(
a
+
b
)
2
−
(
a
−
b
)
2
is
a)
4
a
b
b)
−
4
a
b
c)
2
a
2
+
2
b
2
d)
2
a
2
−
2
b
2
View Solution
Q5
Factorise:
(
a
+
b
)
2
−
2
(
a
2
−
b
2
)
+
(
a
−
b
)
2
View Solution