Ch9

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Chapter 9

Polynomial-Many terms connected with addition or subtraction. Monomial-1 term. Binomial-2 terms connected with addition or subtraction. Trinomial-3 terms connected with addidtion or subtraction. And so on. When you do add or subract these you combine like terms like you would with any other equation. These equations might not be solved, only simplified. 4(a+5b)-6a(2a+1) First we distribute the 4, like usual. 4a+20b-6a(2a+1) Then we distribute 6a. 12a 2 -6a Then we add like terms. -2a-12a 2 +20b is our answer. As stated before, you are just adding like terms, essentially. These can also be in any order, for the most part. Some orders may mess up the answers and therefore cannot be used.
 * Adding and Subtracting Polynomials **

(2y+3)x(y+9) We have 2 binomials, and we need to multiply them. What we do in this situation is we distribute. y(2y+3)+9(2y+3) For these first part, it distributes to 2y 2 +3y The next part distributes to 18y+27. All that is needed now is for them to be added. 2y 2 +21y+27. Another way to do this is the ** Foil method **. (2x-5)(3x+1) We combine the first number of the first binomial with the other parts. 2x(3x)+2x(1) And we do this for the second part as well. -5(3x)+-5(1) All that is left is to simplify both of them and add them together. 5x 2 -12x-5 should be the answer.
 * Multiplying Binomials **

Lets say we have (x+3) 2 This is essentially (x+3)(x+3), so we __//**DO NOT**//__ distribute the exponent. We can then use the foil method or any method really to simplify this binomial. x 2 +6x+9.