आंधी के समय पेड़ के नीचे खड़े क्यों नहीं रहना चाहिए
Answers
Answer:
Factoring x
12
−1 can be tricky but can broken down and worked it out step by step.
Let us recollect some rules:
1. Difference of squares
a
2
−b
2
=(a−b)(a+b)
2. Difference of cubes
a
3
−b
3
=(a−b)(a
2
+ab+b
2
)
3. Sum of cubes
a
3
+b
3
=(a+b)(a
2
−ab+b
2
)
Now let us come to our problem.
x
12
−1
Let us make x
12
into something which we can recognize easily.
x
12
=x
6.2
=(x
6
)
2
We have used a
mn
=(a
m
)
n
(x
6
)
2
−1
2
Now it is form a
2
−b
2
(x
6
−1)(x
6
+1)
Let us factorize x
6
−1
x
6
−1=(x
3
)
2
−1
2
Rewriting x
6
to get into a
2
−b
2
form
x
6
−1=(x
3
−1)(x
3
+1)
x
6
−1=(x−1)(x
2
+x+1)(x+1)(x
2
−x+1)
Now to factorize (x
6
+1)
x
6
+1=(x
2
)
3
+1
3
Rewriting x
6
to get it into a
3
+b
3
form
x
6
+1=(x
2
+1)(x
4
−x
2
+1)
Factors of (x
6
−1)(x
6
+1)
=(x−1)(x
2
+x+1)(x+1)(x
2
−x+1)(x
2
+1)(x
4
−x
2
+1)
Rearranging
(x−1)(x+1)(x
2
+1)(x
2
−x+1)(x
2
+x+1)(x
4
−x
2
+