factorise x8 +1/x8 +1
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Answer:
ANSWER
GIven : x
8
−1
We can further write it as
x
8
−1=(x
4
)
2
−1
2
Based on the equation a
2
−b
2
=(a+b)(a−b)
We get,
x
8
−1=(x
4
+1)(x
4
−1)
x
8
−1=(x
4
+1)((x
2
)
2
−1
2
)
x
8
−1=(x
4
+1)(x
2
+1)(x
2
−1)
So we get
x
8
−1=(x
4
+1)(x
2
+1)(x
2
−1)
By expanding the terms using the formula
We get,
x
8
−1=[(x
2
)
2
+1
2
+2x
2
−2x
2
](x
2
−1)(x+1)(x−1)
On further simplification
x
8
−1=[((x
2
)
2
+1
2
+2x
2
)−2x
2
](x
2
+1)(x+1)(x−1)
Using the formula we get
x
8
−1=(x
2
+1+
2
x)(x
2
+1−
2
x)(x
2
+1)(x+1)(x−1)
Step-by-step explanation:
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