Question

factorise the
a^8-b^8​

Answer 1

Answer:

1.1 Factoring: a8-b8

Theory : 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 : a8 is the square of a4

Check : b8 is the square of b4

Factorization is : (a4 + b4) • (a4 - b4)

Answer 2

the answer is here

(a^4)^2-(b^4)^2

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

(a^2-b^2)(a^2+b^2)(a^4+b^4)

(a-b)(a+b)(a^2+b^2)(a^4+b^4)