Product of Sum and Difference Shortcut

You are doing way too much work if you use the full FOIL method for every single algebra

problem. When you see two brackets that are exactly the same but one has a plus

sign and the other has a minus, you have hit the jackpot. This is the product

of sum and difference shortcut. The middle terms always cancel out to zero,

so you can completely ignore them. Just square the first term, square the last

term, and stick a minus sign in the middle. If you have 3x plus 1 times 3x minus

1, just multiply 3x by itself to get 9x squared, and 1 by 1 to get

1. The answer is 9x squared minus 1. This simple trick cuts your homework