(a+b)^4 +(a-b)(a+b) in factor
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Answers
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Step-by-step explanation:
This is easier than it seems at first glance.
DO NOT multiply out the brackets - that will only make things worse!
This expression is written in the form
x
2
−
y
2
which is difference of 2 squares.
Let (a+b) be
x
and (a-b) be
y
, just to make it easier to work with.
x
4
−
y
4
is also the difference of squares.
(
x
2
)
2
=
x
4
=
(
x
2
+
y
2
)
(
x
2
−
y
2
)
=
(
x
2
+
y
2
)
(
x
+
y
)
(
x
−
y
)
replace
x
and
y
=
[
(
a
+
b
)
2
+
(
a
−
b
)
2
]
[
(
a
+
b
)
+
(
a
−
b
)
]
[
(
a
+
b
)
−
(
a
−
b
)
]
[
(
a
+
b
)
2
+
(
a
−
b
)
2
]
[
(
2
a
)
(
2
b
)
]
=
4
a
b
[
(
a
+
b
)
2
+
(
a
−
b
)
2
]
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