Adding and Subtracting Binomials
Step1
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.
Step2
If you are subtracting, multiply each term in the polynomial being subtracted by -1 in order to turn it into an addition problem. For example, the polynomial (8x^2 + 8) - (x^2 - 2) becomes (8x^2 + 8) + (-x^2 + 2).
Step3
Combine like terms. In the problem above, for example, the x^2 terms are combined and the constant terms are combined giving: (8x^2 + 8) + (-x^2 + 2) = 7x^2 + 10
Multiplying Binomials
Step1
Understand the FOIL method. FOIL is an acronym standing for first, outside, inside, 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 number by the second term of the second number) and so on. It is a great way to ensure that both numbers in the first binomial are multiplied by both numbers in the second.
Step2
Use the FOIL method to multiply the two binomials together. For example, (3x + 4)(3x - 4) = 9x^2 +12x - 12x - 16. Notice that first I multiplied the first term from each binomial expression, then the outside terms and so on.
Step3
Simplify. There will almost always be like terms to combine. In the example above, 12x and -12x cancel out, giving the answer 9x^2 - 16.
Dividing Binomials
Step1
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).
Step2
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 in any other division problem. For example, 20z / 4 = 5z.
Step3
Divide each term in the binomial by the divisor; (18x^3 / 3x) + (9x^2 / 3x) = 6x^2 + 3x.
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