Help me (a)Expand the following expression. (i) (x-4)(x-6)= (ii) (x-2)(x-8)= (b)Hence,factorize(x-2)(x-4)(x-6)(x-8)+16.?

(a)
(i)
(x - 4)(x - 6)
= x^2 - 10x + 24
(ii)
(x - 2)(x - 8)
= x^2 - 10x + 16
(b)
(x - 2)(x - 4)(x - 6)(x - 8) + 16
= (x^2 - 10 x + 20)^2

(i) (x-4)(x-6)
=x(x-6)-4(x-6)
=x^2-6x-4x+24
=x^2-10x+24

(ii) (x-2)(x-8)
=x(x-8)-2(x-8)
=x^2-8x-2x+16
=x^2-10x+16

b)
(x-2)(x-4)(x-6)(x-8)+16
=(x^2-10x+24)(x^2-10x+16)+16
=x^2(x^2-10x+16) -10x(x^2-10x+16) +24(x^2-10x+16) +16
=x^4-10x^3+16x^2 -10x^3+100x^2-160x +24x^2-240x+384+16
=x^4-20x^3+140x^2-400x+400
this cannot be factorized

i) FOIL rule
First: x*x or x^2
Outer: x * (-6) or -6x
Inner: (-4) * x or -4x
Last: (-4)*(-6) or 24
Put them together: x^2 - 6x - 4x + 24. Simplify by combining the middle terms.

ii) FOIL
First: x*x, Outer: x*(-8), Inner: (-2)*x, Last: (-2)*(-8). Put them together, simplify.