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Byju's Answer
Standard VIII
Mathematics
Factorisation Using Algebraic Identities
Match the fol...
Question
Match the following identities:
A
a
2
−
9
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B
a
2
+
4
a
+
4
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C
a
2
−
2
a
+
1
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D
2
(
a
2
+
1
)
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Solution
We know that
(
x
+
y
)
2
=
x
2
+
y
2
+
2
x
y
So,
(
a
+
2
)
2
=
a
2
+
2
2
+
2
×
a
×
2
=
a
2
+
4
+
4
a
We know that
(
x
−
y
)
2
=
x
2
+
y
2
−
2
x
y
So,
(
a
−
1
)
2
=
a
2
+
1
2
−
2
×
a
×
1
=
a
2
+
1
−
2
a
We know that
(
x
+
y
)
(
x
−
y
)
=
x
2
−
y
2
So,
(
a
+
3
)
(
a
−
3
)
=
a
2
−
3
2
=
a
2
−
9
Similarly,
(
a
+
1
)
2
+
(
a
−
1
)
2
=
a
2
+
1
+
2
a
+
a
2
+
1
−
2
a
=
2
a
2
+
2
=
2
(
a
2
+
1
)
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1
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−
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Q.
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