SOLUTION: how do i find the product? {x^2-x+5} {4x^2-2x-1} my guess x^2(4x^2) - x(-2x) 5(1) 4x^4-2x-5-

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: how do i find the product? {x^2-x+5} {4x^2-2x-1} my guess x^2(4x^2) - x(-2x) 5(1) 4x^4-2x-5-       Log On


   

Question 404640: how do i find the product? {x^2-x+5} {4x^2-2x-1}
my guess
x^2(4x^2) - x(-2x) 5(1)
4x^4-2x-5-

Answer by jsmallt9(3758) About Me  (Show Source):
You can put this solution on YOUR website!
%28x%5E2-x%2B5%29%284x%5E2-2x-1%29
To multiply polynomials, you multiply each term of one polynomial by each term of the other polynomial. Then, if there are like terms, you add/subtract the like terms. With 3 terms in both polynomials, we are going to do 9 multiplications!

Before we start, I like to change the subtractions, if any, into additions of the opposite because there are many advantages to having everything an addition:
%28x%5E2%2B+%28-x%29+%2B5%29%284x%5E2%2B+%28-2x%29+%2B+%28-1%29%29
Now we'll start multiplying:


Adding the like terms:
4x%5E4+%2B+%28-6x%5E3%29+%2B+21x%5E2+%2B+%28-9x%29+%2B+%28-5%29

P.S. In response to your thank you note...
The -9x comes from adding the "x" and -10x.