Let's look at (a). The hint suggest writing it as a difference of two squares by adding and subtracting a suitable square. Aboyut the first thing we think of is to add and subtract x^2:

x^4 + 5x^2 + 9 + x^2 - x^2 = (x^4 + 6x^2 + 9) - x^2 = (x^2+3)^2 - x^2 = (x^2+3+x)(x^2+3-x)

For (b) the hint is to add and subtract 4x^2 ...