Factorise : 27a cube - 343b cube
Answers
Answered by
8
Answer:
(3a-7b)(9a^2+21ab+49b^2)
Step-by-step explanation:
27a^3 - 343b^3
= (3a)^3 - (7b)^3
= a^3 - b^3 = (a-b)(a^2 + ab +b^2)
= (3a-7b)(9a^2+21ab+49b^2)
Answered by
1
Answer:
Rewrite
27
x
3
as
(
3
x
)
3
.
(
3
x
)
3
+
343
Rewrite
343
as
7
3
.
(
3
x
)
3
+
7
3
Since both terms are perfect cubes, factor using the sum of cubes formula,
a
3
+
b
3
=
(
a
+
b
)
(
a
2
−
a
b
+
b
2
)
where
a
=
3
x
and
b
=
7
.
(
3
x
+
7
)
(
(
3
x
)
2
−
(
3
x
)
⋅
7
+
7
2
)
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