Question

Lesson 17.2) Model the situation with the sum of polynomials. Simplify their sum. (1 point)3. Vincent is going to frame a rectangular picture with the dimensions shown.Write a polynomial for the perimeter of the frame, and then simplify.5a + 3b2a - 26-I

Answer 1

The perimeter of a rectangle is found adding two times its length to two times its height. In this case, the length measures: 2a - 2b, and the height measures: 5a + 3b, where a and b are two variables. Therefore, the perimeter (P) is:

`\begin{gathered} P=2\cdot\text{length}+2\cdot\text{height} \\ P=2(2a-2b)+2(5a+3b) \\ \text{Distributing:} \\ P=2\cdot2a-2\cdot2b+2\cdot5a+2\cdot3b \\ P=4a-4b+10a+6b \\ \text{Combining similar terms:} \\ P=(4a+10a)+(-4b+6b) \\ P=14a+2b \end{gathered}`