You can if you wish - just keep the soap solution VERY weak or it can burn your plants. I prefer to just blast them off with plain water. Keep in mind that both are attracted to high/excess nitrogen - it's like candy to them - so go easy on the fertilizers.

I had good luck using diatomaceous earth against whiteflies. I was sceptical when my neighbor suggested it, but it provided a long-term (over a year) solution. If your not familiar with it, diatomaceous earth consists of fossilized remains of diatoms, a type of hard-shelled algae.

Because it is approximately 3% magnesium, 33% silicon, 19% calcium, 5% sodium, 2% iron and has many other trace minerals such as titanium, boron, manganese, copper and zirconium, it is a minor fertilizer too. Its a couple of bucks a pound.

Be careful not to breathe the dust, its not toxic, but the particle size can cause lung problems.

Aphids are, as digdirt stated, attracted to parts of plants with lots of Nitrogen, new growth, so being sure your soil is well balanced and plant growth is not overly lush will help. All that needs be done to control them is a sharp stream of water, from your hose or from a spray bottle. Nothing stronger is really needed.
Whitefly can be controlled by insecticidal soap sprays, 1 teaspoons of soap in 1 quart of water.

Here is a link that might be useful: About Whitefly

Beware on the insecticidal soap directions. The amount of product per gallon will depend upon the brand that you purchase. Insecticidal soaps are very effective and efficient, but the label needs to be read carefully before applying.

belle, liquid dish detergents are not true 'soaps', and can actually be much more caustic on our plants than commercial insecticidal soaps. Plus, the many additive can also cause problems....for the plant, that is, and without necessarily controlling your pests! Yikes!

If the aphids are really bad, you can use the insecticidal soap on them, too. Get them under control before they take over your part of the world.

The old "sharp blast of water" is as useful as teets on a boar hog. Maybe it will work on a potted plant. That's about it. If you have a medium to large garden good luck.

I'd like to see ol' girl running around a Texas size garden with a "sharp blast of water". Eat a bowl of beans and give 'em a sharp blast of gas. Just as effective.

What is needed in the Insecticidal Soap mixture is a 1 percent mix of soap in water and it does need to be real soap, soap made by reacting animal fat with lye. The mixture is 1 teaspoon of that real soap in 1 quart of water and it does not make any difference which soap is used.
So, mojo, why do your think the sharp blast of water is ineffective when people around the world have used it successfully to control aphids?

So, Kimmsr, you are talking about a home remedy mixture using a soap, rather than a dish detergent, right? You might want to explain what these 'real soaps' are and where to get them, as I'd wager that most people have NO idea what you mean. (I know, but a lot of people won't. It's worthy being a bit more expansive on the subject.)

I'd suggest that using a COMMERCIAL insecticidal soap, manufactured specifically for this purpose is a lot more economical and probably more efficient than the home remedy.

mojo, you may not have the patience or interest to keep aphids at bay with strong streams of water. But it does work.....at keeping a population under control. It's a viable, chemical-free option.