Question

factorise a^8-a^2b^6​

Answer 1

Answer:

Step-by-step explanation:

a2a6−a2b6

=a2(a6−b6), here a2 is common between the terms

=a2(a3×2−b3×2)

=a2[(a3)2−(b3)2]

This is of the form x2−y2=(x−y)(x+y),where x=a3 and y=b3

=a2(a3−b3)(a3+b3)

Now we factorize (a3−b3) and (a3+b3):

We know that (a3−b3)=(a−b)(a2+ab+b2)

And (a3+b3)=(a+b)(a2−ab+b2)

Then,

a2(a3−b3)(a3+b3)=a2(a−b)(a2+ab+b2)(a+b)(a2−ab+b2)