How Do You Solve a Word Problem by Subtracting Polynomials?

The length is y²+3y+7
The width is y-3
Finding the difference means we are going to subtract
Distribute the negative through the second set of parentheses
3y and -y are like terms
7 and 3 are also like terms
3y-y=2y
7+3=10
Since there are no more like terms to combine and no parentheses, the polynomial is in simplest form

1. Remember, difference means subtraction
1. The length of the frame is y²+3y+7
2. The width of the frame is y-3
3. Subtracting these two polynomials will give us the difference
1. The length of the frame is y²+3y+7
2. The width of the frame is y-3
3. Subtracting these two polynomials will give us the difference
1. To simplify, we need to get rid of the parentheses
2. We'll need to distribute the negative in front of the second set of parentheses
1. We can't get rid of the parentheses until we do this
1. Since there is no negative in front of the first set of parentheses, we don't need them
1. This means we will flip the sign of each term inside the parentheses
2. So y becomes -y
3. And -3 becomes 3
1. Now we can write -y+3 without parentheses
1. To get our polynomial in simplest form, we need to combine like terms
2. Remember, like terms have the same variables raised to the same power
1. 3y and -y both have y raised to the first power
2. So they are like terms that we can combine
1. Neither 7 nor 3 has a variable
2. So they are like terms as well
1. Combine the like terms to simplify
2. The like terms 3y and -y combine to make 2y
3. The like terms 7 and 3 combine to make 10
1. Since there are no parentheses and no more like terms to combine, our polynomial is in simplest form

A picture frame has the dimensions given in the diagram. Determine how much the longer the length is than the width. Write your answer as a polynomial in simplest form.