Q.III(A) Factorize & Division of algebraic expression
1. 5ac²+2acd-10bcd-4bd²
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Answer:
x
2
+
6
x
+
9
We see that there are no common factors for the three terms in the expression.
However, in the expression, we see that
9
is a perfect square.
In this case, we seek the help of algebraic identities to factorize the expression easily.
This expression looks similar to the identity:
(
a
+
b
)
2
=
a
2
+
2
a
b
+
b
2
Comparing the given expression to the identity, we get
a
=
x
,
b
=
3
Therefore, the factors are
(
x
+
3
)
2
or
(
x
+
3
)
(
x
+
3
)
Example 2
16
x
2
−
25
y
2
In this expression, we see that there are no common factors.
Also, we see that this expression is of the form:
a
2
−
b
2
=
(
a
+
b
)
(
a
−
b
)
Comparing the given expression to the identity, we get
a
=
4
x
,
b
=
5
y
Therefore, the factors are
(
4
x
+
5
y
)
(
4
x
−
5
y
)
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