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Byju's Answer
Standard VII
Mathematics
(a+b)(a-b) Expansion and Visualisation
Find the HCF ...
Question
Find the HCF of the following pair of polynomials:
x
2
−
x
y
−
2
y
2
and
x
2
+
3
x
y
+
2
y
2
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Solution
We know that
H
C
F
is the highest common factor.
Factorise
x
2
−
x
y
−
2
y
2
as follows:
x
2
−
x
y
−
2
y
2
=
x
2
−
2
x
y
+
x
y
−
2
y
2
=
x
(
x
−
2
y
)
+
y
(
x
−
2
y
)
=
(
x
+
y
)
(
x
−
2
y
)
Now,
factorise
x
2
+
3
x
y
+
2
y
2
as follows:
x
2
+
3
x
y
+
2
y
2
=
x
2
+
2
x
y
+
x
y
+
2
y
2
=
x
(
x
+
2
y
)
+
y
(
x
+
2
y
)
=
(
x
+
y
)
(
x
+
2
y
)
Since the common factor between the polynomials
x
2
−
x
y
−
2
y
2
and
x
2
+
3
x
y
+
2
y
2
is
(
x
+
y
)
.
Hence, the
H
C
F
is
(
x
+
y
)
.
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