brushing dog's teeth

I've been brushing my dog's teeth 1 or 2 times a week, Also give him Greenies every other day or so.  I'm using dog toothpaste, but it's pretty expensive.  Will baking soda hurt a dog?  I use it on my own teeth sometimes.  It does a great job of cleaning teeth, but am hesitant to use it on Quincy.  Anyone know?

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