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Byju's Answer
Standard VIII
Mathematics
Algebraic Identities
State whether...
Question
State whether the statement is True or False:
(
2
a
+
3
)
(
2
a
−
3
)
(
4
a
2
+
9
)
is equal to
16
a
4
−
81
.
A
True
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B
False
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Solution
The correct option is
A
True
Given,
(
2
a
+
3
)
(
2
a
−
3
)
(
4
a
2
+
9
)
.
We know,
(
a
+
b
)
(
a
−
b
)
=
(
a
2
−
b
2
)
.
Multiply by using direct method, we get,
(
2
a
+
3
)
(
2
a
−
3
)
(
4
a
2
+
9
)
=
[
(
2
a
)
2
−
(
3
)
2
]
(
4
a
2
+
9
)
=
(
4
a
2
−
9
)
(
4
a
2
+
9
)
=
(
4
a
2
+
9
)
(
4
a
2
−
9
)
.
Now, by using formula
(
a
2
−
b
2
)
=
(
a
+
b
)
(
a
−
b
)
, we get,
=
(
(
4
a
2
)
2
−
(
9
)
2
)
=
16
a
4
−
81
.
Hence, the statement is true.
Therefore, option
A
is correct.
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