Factorize :- i) 64x3 − 27 y 3
Answers
Answered by
0
Answer:
This expression is a
sum of cubes
and is factorised as follows
∣
∣
∣
∣
¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯
a
a
a
3
+
b
3
=
(
a
+
b
)
(
a
2
−
a
b
+
b
2
)
a
a
∣
∣
−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−
now
64
x
3
=
(
4
x
)
3
and
27
y
3
=
(
3
y
)
3
For factorising purposes a = 4x and b = 3y
⇒
64
x
3
+
27
y
3
=
(
4
x
+
3
y
)
(
16
x
2
−
12
x
y
+
9
y
2
)
I hope it helps you
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Answered by
0
First, we know that the way to factor difference of cubes is:
a
3
−
b
3
=
(
a
−
b
)
(
a
2
+
a
b
+
b
2
)
Following this, we first know that:
3
√
64
x
3
=
4
x
and
3
√
27
y
3
=
3
y
Based on this, we know that:
a
2
=
(
4
x
)
2
=
16
x
2
and
b
2
=
(
3
y
)
2
=
9
y
2
Lastly, we know that:
a
b
=
(
4
x
)
(
3
y
)
=
12
x
y
Combining all this together, we know that the factored form is:
(
4
x
−
3
y
)
(
16
x
2
+
12
x
y
+
9
y
2
)
Hope this helps!
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