Can someone help me with this question from lb5?

I feel like I understand and do not understand at the same time. I start to lose it from the point of square root of a^8. Can a kind soul help me to unpack from there? Thanks!

Can someone help me with this question from lb5?

I feel like I understand and do not understand at the same time. I start to lose it from the point of square root of a^8. Can a kind soul help me to unpack from there? Thanks!

Hint:

a^8 = (a^4)^2

Okay I think I got it

but do you mind to share more about the root a^8? that part I still do not fully get it. Thank you in advance!

Sorry, not sure what the problem is (be detailed).

This part - Note that = root (a^8) = (a8)½ = a^4. How does this part relate with the factorisation? Or to be more precise, wouldn’t introducing the square root impact the numerator and denominator. I am unsure how to relate it with the solution. Unlike the earlier solution, it was merely converting from one algebraic expression to another algebraic expression.

I think they are just saying that because (for a \geq 0)

\sqrt{a^8} = a^4

you can write (by squaring both sides)

a^8 = (a^4)^2

and proceed as you did earlier. Does that help?

Ohhh they are just merely substituting this expression of a^8 - b^8 with (a^8-b^8)^1/2 = a^4 - b^4