Simplify the following product:
(x+
x
1
)(x−
x
1
)(x
2
+
x
2
1
)
- A(x+
x
1
)
4 - Bx
4
+
x
4
1
- C(x−
x
1
)
4 - Dx
4
−
x
4
1
Solution & Step-by-step Explanation
Using the algebraic identity (a+b)(a−b)=a
2
−b
2
:
First, multiply the first two terms:
(x+
x
1
)(x−
x
1
)=x
2
−
x
2
1
Now substitute this back into the expression:
(x
2
−
x
2
1
)(x
2
+
x
2
1
)
Apply the same identity again where a=x
2
and b=
x
2
1
:
(x
2
)
2
−(
x
2
1
)
2
=x
4
−
x
4
1
2
−b
2
:
First, multiply the first two terms:
(x+
x
1
)(x−
x
1
)=x
2
−
x
2
1
Now substitute this back into the expression:
(x
2
−
x
2
1
)(x
2
+
x
2
1
)
Apply the same identity again where a=x
2
and b=
x
2
1
:
(x
2
)
2
−(
x
2
1
)
2
=x
4
−
x
4
1