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3 votes
Factorise: a8 - b8


please solve this​

User Huron
by
8.3k points

1 Answer

3 votes

Answer:

(a - b)(a + b)(a² + b²)(
a^(4) +
b^(4) )

Explanation:

by repeated use of the difference of squares factorising method, that is

a² - b² = (a - b)(a + b)

given


a^(8) -
b^(8)

= (
a^(4) )² - (
b^(4)

= (
a^(4) -
b^(4) )(
a^(4) +
b^(4) ) ← factor left parenthesis using difference of squares

= ( a² - b²)(a² + b²)(
a^(4) +
b^(4) ) ← factor left parenthesis by difference of squares

= (a - b)(a + b)(a² + b² )(
a^(4) +
b^(4) )

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