square of a binomial

Squaring a binomial means multiplying it by itself, and it follows a fixed, memorable pattern: (a + b)^2 = a^2 + 2ab + b^2. In words — square the first term, square the last term, and sandwich twice their product in the middle.

If you ever forget the formula, just FOIL it out: (a + b)(a + b) = a^2 + ab + ba + b^2, and the two middle terms ab and ba are like terms that add to 2ab. The difference version works the same way: (a - b)^2 = a^2 - 2ab + b^2, with only the middle sign changing.

The single biggest pitfall in all of beginning algebra is writing (a + b)^2 = a^2 + b^2. That is wrong — it silently throws away the 2ab term. Squaring is not distributive over addition; whenever you square a sum, the cross term 2ab must appear.