hi bobbym here Agnishom solve all the problems and he also given hints. i think still you have some confusion.I will explain clearly along with formulas

problem:x^4+8x^2+144

solution: [(x^2)^2+2(x^2)(12)+(12)^2]-16x^2 Formula:(a+b)^2=a^2+2ab+b^2

here (x^2+12)^2 = (x^2)^2+2(x^2)(12)+12^2

If u solve this, the result be x^4+24x^2+144

But in the given question we have 8x^2, we got 24x^2 for that we are subtracting 16x^2 from our result

so the equation be [(x^2)^2+2(x^2)(12)+12^2]-16x^2

[(x^2+12)^2]-16x^2

(x^2+12)^2-(4x)^2 Formula(a+b)(a-b)=a^2-b^2

here a=x^2+12 b=4x, [x^2+12+4x][x^2+12-4x]

Therefore[x^2+4x+12][x^2-4x+12]