maths!!!!!!!!!!!!!!!!!

Suppose P(x)=x^n - a^n and Q(x)=x^n + a^n wheree a is an integer and n is a positive integer.
(a)Find the value of P(a).
P(a)=a^n-a^n=0//

(b)Hence deduce that P(x) is divisible by x-a.
∵P(a)=0


∴P(x) is divisible by x-a.



(c)if n is an odd number,find the value of Q(-a).
∵Q(x)=x^n + a^n

∴Q(-a)=(-a)^n+a^n=-a^n+a^n=0//


(d)Hence deduce that Q(x) is divisible by x+a if n is an odd number.

∵Q(a)=0


∴Q(x) is divisible by x-a if n is an odd number.

e)Using the above results.show that both 2222^5555 + 4^5555 and 5555^2222 - 4^2222 are divisible by 7.

P(x)=x^n - a^n

Accroding (a) and (b)

P(x) is divisible by x-a.

5555^2222 - 4^2222 are ivisible by 7
and

Accroding (c) and (b)

Q(x) is divisible by x-a.

2222^5555 + 4^5555 are divisible by 7.

(f)Hence show that 2222^5555 + 5555^2222 is divisible by 7.
let 2222^5555 + 4^5555=7M

and 5555^2222 - 4^2222=7N

2222^5555 + 5555^2222
=7M+7N
=7(M+N)
∴2222^5555 + 5555^2222 is divisible by 7.