Algebra 2 questions I NEED HELP ASAP!!!

Question

Emma is designing a rectangular garden and wants to create a walkway around it. The length of the garden is given by the expression L(x) = 3x² + 2x + 1 and the width is given by W(x) = 2x² — x + 3. 

She decides to calculate the area of the garden by multiplying the polynomials. What is the area of the garden?

Answer 1

Hi Lamya,

Area of Rectangle = Length * Width

You were asked for an area and given a length and a width, so multiply:

A = (3x^2 + 2x + 1)(2x^2 - x - 3)

A = 6x^4 - 3x^3 - 9x^2 + 4x^3 - 2x^2 - 6x + 2x^2 - x - 3

Combine like terms:

A = 6x^4 + x^3 - 9x^2 - 7x - 3

Answer 2

All we need to do is multiply the polynomials together, which is done by setting the following up:

(3x^2+2x+1)(2x^2-x+3)

Now, we choose a specific term to start with, 3x^2 for example, and multiply it by each term in the second polynomial. Do this for the other two terms in the first polynomial and add the resulting terms (there should be 9 without any reduction)