What polynomial in standard form represents the area if the stamp?

Question

You are designing a rectangular rubber stamp. The length of the stamp is 2r+3. The width of the stamp is r-4.

Answer 1

The area of a rectangle is given by the formula length x width.

 

We have an expression for the length: 2r + 3

And we have an expression for the width: r - 4

 

If we multiply those two expressions together, we will have the area:

 

Area = length x width

Area = (2r + 3) x (r - 4)

 

Now we use the distributive property of multiplication and associative property of addition:

 

(2r + 3) x (r - 4) = r(2r + 3) - 4(2r + 3)

 

Multiply everything out:

 

2r² + 3r - 8r - 12

 

Finally, combine like terms:

 

2r² - 5r - 12