Question

⚅⚅⚅⚅ HELP ⚅⚅⚅⚅

⚘⚘ FACTORISE ⚘⚘


( x^12 - 1 )

Answer 1

❤❤here is your answer ✌ ✌

Let us recollect some rules. ohk

Difference of squares
➡a2−b2=(a−b)(a+b)

Difference of cubes 
➡a3−b3=(a−b)(a2+ab+b2)

Sum of cubes
➡a3+b3=(a+b)(a2−ab+b2)

Now let us come to our problem.

x12−1
Let us make x^12 into something which we can recognize easily.

x12=x6⋅2=(x6)2 We have used amn=(am)n

(x6)2−12 Now it is of form a2−b2

(x6−1)(x6+1)

Let us factorize x6−1

x6−1=(x3)2−12 Rewriting x6 to get into a2−b2 form
x6−1=(x3−1)(x3+1)
x6−1=(x−1)(x2+x+1)(x+1)(x2−x+1)

Now to factorize (x6+1)
x6+1=(x2)3+13 Rewriting x6 to get it into a3+b3 form
x6+1=(x2+1)(x4−x2+1)

Factors of (x6−1)(x6+1)
=(x−1)(x2+x+1)(x+1)(x2−x+1)(x2+1)(x4−x2+1)

Rearranging
(x−1)(x+1)(x2+1)(x2−x+1)(x2+x+1)(x4−x2+1)

I hope it help you

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⤵⤵⤵

Answer 2

Step-by-step explanation:

let us come to our problem.

x12−1

Let us make x^12 into something which we can recognize easily.

x12=x6⋅2=(x6)2 We have used amn=(am)n

(x6)2−12 Now it is of form a2−b2

(x6−1)(x6+1)

Let us factorize x6−1

x6−1=(x3)2−12 Rewriting x6 to get into a2−b2 form

x6−1=(x3−1)(x3+1)

x6−1=(x−1)(x2+x+1)(x+1)(x2−x+1)

Now to factorize (x6+1)

x6+1=(x2)3+13 Rewriting x6 to get it into a3+b3 form

x6+1=(x2+1)(x4−x2+1)

Factors of (x6−1)(x6+1)

=(x−1)(x2+x+1)(x+1)(x2−x+1)(x2+1)(x4−x2+1)

Rearranging

(x−1)(x+1)(x2+1)(x2−x+1)(x2+x+1)(x4−x2+1)

I hope it help you