27+-+Sec.+10.2A

[|practice problems]

Multiplying polynomials Carlos F. James R · There were two formats for [|adding and subtracting polynomials] : "horizontal" and "vertical". You can use those same two formats for multiplying polynomials. The very simplest case for polynomial multiplication is the product of two one-term polynomials. For instance: I've already done this type of multiplication when I was first learning about [|exponents], [|negative numbers] , and [|variables]. I'll just apply the rules I already know: (5//x^//2)(–2//x^//3) = **–10//x^//5** The next step up in complexity is a one-term polynomial times a multi-term polynomial. For example: To do this, I have to distribute the –3//x// through the [|parentheses]  : –3//x//(4//x^//2 – //x// + 10) = –3//x//(4//x^//2) – 3//x//(–//x//) – 3//x//(10) = **–12//x^//3 + 3//x^//2-30x**
 * ** Simplify (5//x//2)(–2//x//3) **
 * ** Simplify –3//x//(4//x^//2 – //x// + 10) **

http://www.algebralab.org/practice/practice.aspx?file=Algebra1_10-2_10-3.xml

EXAMPLES:

1.( //x// + 3 )( //x// + 2 ) (x + 3)(x) + (x + 3)(2) x(x) + 3(x) + x(2) + 3(2) = x^2 + 5x + 6

2. (3x - 2) (2x + 7) = 3x(2x+7) - 2(2x + 7) = (3x) (2x) + (3x) (7) - (2) (2x) -2(7)

6x^2 + 21x -4x -14 = 6x^2+17x-14
3. (6x + 5) (x^2 - 3x) = 6x(x^2 - 3x) + 5(x^2 - 3x) = 6x (x^2) -6x(3x) + 5(x^2) -5(3x)

6x^3 -13x^2 -15x
Practice problem

1. (8x)(4x+6)

2.-3x(4x^2 -x + 10)