Question

Essay: Show all work.

A school designer wants to create a whiteboard with the optimal dimensions to enhance learning. It is determined that if one side of the whiteboard is x+2y inches, the other side should be x^2+3xy-4y^2 inches. Write an algebraic expression for the area of such a whiteboard, simplify it, and include correct units with your solution.

Can you walk me through, what is the expression first.
is it:
(x+2y)(x^2+3xy-4y^2)

Answer 1

You have to write an essay on this?

Answer 2

No I think it just gets graded differently. I have to show work, write it out.

Answer 3

I see

Answer 4

You just have to multiply it out and reduce

Answer 5

Since you are dealing with multiplying polynomials, you have to take each term in the right and multiply it by each term in the left, then combine them.
So, you take ((x(x^2))+(x(3xy)-(x(4y^2)) + ((2y(x^2)+2y(3xy)-(2y(4x^2)) which gives \[x^3+3x^2y^2+2x^2y+6xy^2-8y^3\].
This is as simplified as it gets and, since you are looking for an area, your unit will be in inchs^2

Answer 6

This is what I got:
(x+2y)(x^2+3xy-4y^2)
x(x^2+3xy-4y^2) +2y(x^2+3xy-4y^2)
x(x^2)+x(3xy)+x(-4y^2)+2y(x^2)+2y(3xy)+2y(-4y^2)
x^3+3x^2y-4xy^2+2yx^2+6xy^2-8y^3
=x^3-8y^3+5yx^2-2xy^2

Answer 7

Although the steps are provided correctly, the final answer given above is not right.

I have posted the answer and the steps at http://www.oojih.com/show/algebra/polynomials/

scroll down to comment section to see the steps and explanation

Answer 8

\begin{gather} (x+2y) * (x^2+3xy-4y^2) \cr x(x^2+3xy-4y^2) + 2y (x^2+3xy-4y^2) \cr x^3 + 3x^2y - 4xy^2 + 2x^2y + 6xy^2 - 8y^3 \cr x^3 + 5x^2y + 2xy^2 - 8y^3 \end{gather}