Binomials are polynomial equations with only two terms. They are easier to deal with than polynomials, which have more terms, but they can still get confusing if you fail to follow some basic rules. Students typically will need to master binomials as they enter algebra classes.
Adding and Subtracting Binomials
Arrange each term in each binomial in order of degree from greatest to least. The degree of a binomial is the exponent attached to the term. For example, 4x^2 is a second degree term.
Multiply each term in the binomial that is being subtracted by -1 to turn it into an addition problem. For example, the problem (8x^2 + 8) - (x^2 - 2) becomes (8x^2 + 8) + (-x^2 + 2).
Combine like terms. In the example problem, the x^2 terms are combined and the constant terms are combined, yielding (8x^2 + 8) + (-x^2 + 2) = 7x^2 + 10.
Understand the F.O.I.L. method. F.O.I.L. is an acronym standing for first, outside, inside and last. It means that you multiply the first number of the first binomial by the first number of the second, then the numbers on the outside (the first term of the first binomial by the second term of the second binomial) and so on. This ensures that both numbers in the first binomial are multiplied by both numbers in the second.
Use the F.O.I.L. method to multiply the two binomials together. For example, (3x + 4)(3x - 4) = 9x^2 +12x - 12x - 16. Notice that -12x is the product of the outside terms and -16 is the product of the last terms, 4 and -4.
Simplify. There will almost always be like terms to combine. In the example, 12x and -12x cancel out, yielding the answer 9x^2 - 16.
Use the distributive property to divide both terms in the binomial by the monomial divisor. For example, (18x^3 + 9x^2) / 3x = (18x^3 / 3x) + (9x^2 / 3x).
Understand how to divide by a term. If you are dividing a higher order term by a lower order term, you subtract the exponent. For example, y^3/y = y^2. The number part of each term is handled like any other division problem. For example, 20z / 4 = 5z.
Divide each term in the binomial by the divisor; (18x^3 / 3x) + (9x^2 / 3x) = 6x^2 + 3x.