I recently had a question from a question about squaring a binomial. The specific problem was
(2x + 7)^2.  He said the answer was 4x^2 + 49. This is incorrect and a very common mistake that I see.  What he did was simplify (2x)^2 + (7)^2, but (2x + 7)^2 is not the same as (2x)^2 + (7)^2. 

If we take 4^2, for example, that's 4 times 4. So (2x + 7)^2 is (2x + 7)(2x + 7). From here we have to use the FOIL method to multiply, which is (2x)(2x) + (2x)(7) + (7)(2x) + (7)(7).

Multiply and simplify to get 4x^2 + 28x + 49.