Multiplying Polynomials Special Products By Johnny W Arthur

Multiplying Polynomials & Special Products By; Johnny W. , Arthur S. , And Isiah C. S

Objectives S 1. Evaluate f(x) x g(x) for a given x S 2. Multiplying two polynomial functions S 3. Square a binomial S 4. Find the product of two binomials as a difference of squares

A Polynomial Example

Binomial S A binomial is a polynomial with two terms

Product In Algebra xy means x multiplied by y Likewise (a+b)(a−b) means (a+b) multiplied by (a−b), which we will be using a lot here!

Special Binomial Products S So when we multiply binomials we get. . . Binomial Products! S And we will look at three special cases of multiplying binomials. . . so they are Special Binomial Products.

Multiplying A Binomial By Itself S (a+b)2 = (a+b) =. . . ?

Simplifying Polynomials Simplify (5 x 2)(– 2 x 3)

Answer S (5 x 2)(– 2 x 3) = – 10 x 5

One Term Poloynomial S Simplify – 3 x(4 x 2 – x + 10) S To do this , I have to distribute the -3 x through the parentheses

One Term Polynomials S – 3 x(4 x 2 – x + 10) S = – 3 x(4 x 2) – 3 x(–x) – 3 x(10) S = – 12 x 3 + 3 x 2 – 30 x

Two Terms Polynomials S The next step up is a two-term polynomial times a two- term polynomial. This is the simplest of the "multi-term times multi-term" cases. There actually three ways to do this. Since this is one of the most common polynomial multiplications that you will be doing

Two Term Polynomial S Simplify (x + 3)(x + 2) The first way I can do this is "horizontally"; in this case, however, I'll have to distribute twice, taking each of the terms in the first parentheses "through" each of the terms in the second parentheses:

Two Term Polynomial S (x + 3)(x + 2) S = (x + 3)(x) + (x + 3)(2) S = x(x) + 3(x) + x(2) + 3(2) S = x 2 + 3 x + 2 x + 6