Question 404640
{{{(x^2-x+5)(4x^2-2x-1)}}}
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!<br>
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:
{{{(x^2+ (-x) +5)(4x^2+ (-2x) + (-1))}}}
Now we'll start multiplying:
{{{x^2*4x^2 + x^2*(-2x) + x^2*(-1) + (-x)(4x^2) + (-x)(-2x) + (-x)(-1) + 5(4x^2) + 5(-2x) + 5(-1)}}}
{{{4x^4 + (-2x^3) + (-x^2) + (-4x^3) + 2x^2 + x + 20x^2 + (-10x) + (-5)}}}
Adding the like terms:
{{{4x^4 + (-6x^3) + 21x^2 + (-9x) + (-5)}}}<br>
P.S. In response to your thank you note...
The -9x comes from adding the "x" and -10x.