a,
`A=(x-4)^2 + 8(x-4) + 16`
`=> A =(x-4 + 4)^2 = x^2`
b,
`B=25-10(2x+5) + (2x+5)^2`
`=> B=(5-2x-5)^2=(-2x)^2 = 4x^2`
c,
`C=(3x-1)^2 + 2(3x-1)(x+1) + (x+1)^2 `
`=> C=(3x-1+x+1)^2 = (4x)^2 = 16x^2`
d,
`D=(a-1)(a+1)(a^2+1)(a^4+1)(a^8+1)`
`=>D=(a^2-1)(a^2+1)(a^4+1)(a^8+1)`
`=>D=(a^4-1)(a^4+1)(a^8+1)`
`=>D=(a^8-1)(a^8+1)`
`=>D=a^16 - 1`