Factorise the following expression 36x2+96xy+64y2
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Answer:
Note that all of the coefficients are divisible by
4
, so we can separate that out as a scalar factor. Then noticing that the first and last terms are perfect squares, we find that the middle term matches the pattern:
a
2
+
2
a
b
+
b
2
=
(
a
+
b
)
2
with
a
=
3
x
and
b
=
4
y
as follows:
36
x
2
+
96
x
y
+
64
y
2
=
4
(
9
x
2
+
24
x
y
+
16
y
2
)
=
4
(
(
3
x
)
2
+
2
(
3
x
)
(
4
y
)
+
(
4
y
)
2
)
=
4
(
3
x
+
4
y
)
2
Step-by-step explanation:
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