The binomial formulas are
and may be any variables, or even more general expressions. The expression on the left of the first and second binomial formulas are perfect squares, the expression on the left of the third formula is the difference of (two) squares.
Note that the first and second binomial formulas are equivalent. Just replace with to get from one to the other.
It is straightforward to verify the binomial formulas from left to right using the distributive law. For example:
Of the above, equations , , , , and are typical for the kind of operations that occur in the solution of quadratic equations. The equation describes a critical step in the derivation of the quadratic formula . The other equations described steps that may occur in factoring
You can find many more examples in any textbook on Intermediate Algebra. Look for terms like solving quadratic equations, binomial formulas, perfect squares, completing the square.