(a ^ 3 + b ^ 3)/(a ^ 2 + 2ab + b ^ 2) × (a ^ 2 - b ^ 2)/(a - b)
Answers
Answered by
0
=
2
a
b
2
Explanation:
The first step in algebraic fractions is to factorise wherever possible.
(
2
a
2
+
a
b
−
b
2
)
(
a
3
+
b
3
)
÷
(
2
a
2
b
2
−
a
b
3
)
(
2
a
2
−
2
a
b
+
2
b
2
)
quadratic trinomial
sum of cubes
÷
common factor
common factor
=
(
2
a
−
b
)
(
a
+
b
)
(
a
+
b
)
(
a
2
−
a
b
+
b
2
)
÷
a
b
2
(
2
a
−
b
)
2
(
a
2
−
a
b
+
b
2
)
To divide: multiply by the reciprocal
=
(
2
a
−
b
)
(
a
+
b
)
(
a
+
b
)
(
a
2
−
a
b
+
b
2
)
×
2
(
a
2
−
a
b
+
b
2
)
a
b
2
(
2
a
−
b
)
Cancel like factors
=
(
2
a
−
b
)
(
a
+
b
)
(
a
+
b
)
(
a
2
−
a
b
+
b
2
)
×
2
(
a
2
−
a
b
+
b
2
)
a
b
2
(
2
a
−
b
)
=
2
a
b
2
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