Advertisements
Advertisements
Question
Factorize each of the following expression:
x8 − 1
Advertisements
Solution
\[x^8 - 1\]
\[ = ( x^4 )^2 - 1^2 \]
\[ = ( x^4 - 1)( x^4 + 1)\]
\[ = [( x^2 )^2 - 1^2 ]( x^4 + 1)\]
\[ = ( x^2 - 1)( x^2 + 1)( x^4 + 1)\]
\[ = ( x^2 - 1^2 )( x^2 + 1)( x^4 + 1)\]
\[ = (x - 1)(x + 1)( x^2 + 1)( x^4 + 1)\]
APPEARS IN
RELATED QUESTIONS
Factorize each of the following expression:
a4 − 16b4
Factorize each of the following expression:
25x4y4 − 1
Factorize each of the following expression:
a4 − (2b + c)4
Factorize each of the following expression:
(3x + 4y)4 − x4
Factorize each of the following expression:
a4b4 − 16c4
Factorize each of the following expression:
x − y − x2 + y2
Factorize each of the following quadratic polynomials by using the method of completing the square:
p2 + 6p + 8
Factorize each of the following quadratic polynomials by using the method of completing the square:
q2 − 10q + 21
Factorize each of the following quadratic polynomials by using the method of completing the square:
a2 + 2a − 3
Factorize each of the following quadratic polynomials by using the method of completing the square:
y2 − 7y + 12
