Definition: A binomial is a polynomial with exactly two unlike terms, such as 3x + 5 or a^2 – 9b, joined by addition or subtraction.
What is a binomial?
The prefix bi means two. The two terms cannot be combined, because their variable parts differ. The expression 4x + 7x is not a binomial; it simplifies to the monomial 11x.
How do you multiply binomials?
Multiply each term in the first by each term in the second, then combine like terms. A box or the FOIL method keeps track of the four products.
Example. (2x + 5)(x – 7) = 2x2 – 14x + 5x – 35 = 2x2 – 9x – 35.
What about squaring a binomial?
The square (x + 6)2 means (x + 6)(x + 6), which equals x2 + 12x + 36. It does not equal x2 + 36. The middle term 12x comes from two equal cross products. Forgetting it is the most common binomial error. Special products such as the difference of squares and the perfect square trinomial grow out of binomial multiplication, and recognizing them saves time when you factor.