25x^3+125y^3 please factorize
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Answered by
0
Answer:
Answer:
27
x
3
−
125
y
3
=
(
3
x
−
5
y
)
(
9
x
2
+
15
x
y
+
25
y
2
)
Explanation:
Notice that both of the terms are perfect cubes:
27
x
3
=
(
3
x
)
3
125
y
3
=
(
5
y
)
3
So we can conveniently use the difference of cubes identity:
A
3
−
B
3
=
(
A
−
B
)
(
A
2
+
A
B
+
B
2
)
with
A
=
3
x
and
B
=
5
y
as follows:
27
x
3
−
125
y
3
=
(
3
x
)
3
−
(
5
y
)
3
=
(
3
x
−
5
y
)
(
(
3
x
)
2
+
(
3
x
)
(
5
y
)
+
(
5
y
)
2
)
=
(
3
x
−
5
y
)
(
9
x
2
+
15
x
y
+
25
y
2
)
The remaining quadratic factor has no linear factors with Real coefficients. If we allow Complex coefficients then we can factor a little further:
=
(
3
x
−
5
y
)
(
3
x
−
5
ω
y
)
(
3
x
−
5
ω
2
y
)
where
ω
=
−
1
2
+
√
3
2
i
is the primitive Complex cube root of
1
.
Step-by-step explanation:
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Answer:
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