Question

x⁸-1 Factorise Completely​

Answer 1

How to solve your problem

8−1

x^{8}-1x8−1

Grouping

1

Find one factor

Factor by grouping

Factor by grouping

Factor by grouping

(−1)(7+6+5+4+3+2

Answer 2

Answer:

: A difference of two perfect squares, A2 - B2 can be factored into (A+B) • (A-B)

Proof : (A+B) • (A-B) =

A2 - AB + BA - B2 =

A2 - AB + AB - B2 =

A2 - B2

Note : AB = BA is the commutative property of multiplication.

Note : - AB + AB equals zero and is therefore eliminated from the expression.

Check : 1 is the square of 1

Check : x8 is the square of x4

• Factorization is : (x4 + 1) • (x4 - 1)