Question

factorise x⁸-1
points points points​

Answer 1

Answer:

$\huge\fbox\colorbox{pink}{✿Yøur-An˜swer♡}$(x⁴+1) (x²+1) (x+1) (x-1)

Step-by-step explanation:

x⁸-1=(x⁴)²-(1)²

=(x⁴+1) [(x²)²-(1)²]

=(x⁴+1) (x²+1) (x²-1)

=(x⁴+1) (x²+1) (x²-1²)

=(x⁴+1) (x²+1) (x+1) (x-1)

$\huge\color{pink}{°•✩shravyanb✩°•}$

Answer 2

x8−1=(x2+1+2 x)(x2+1−2 x)(x2+1)(x+1)(x−1)

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−