Question

representing perimeter using a polynomial expression
the perimeter formula for a rectangle is ( 2l + 2w ), where ( l ) is the length and ( w ) is the width. complete the steps to find an expression that represents the perimeter of the rectangle.

1. substitute the expressions for length and width into the formula ( 2l + 2w ).
2. distribute 2 to each term in the parentheses.

( 2(8x - 1)+2x + 4 )
( 2(8x - 1)+2(2x + 4) )
( 2(8x)-1 + 2(2x)+4 )

Explanation:

Step1: Substitute length and width

Substitute \(l = 8x - 1\) and \(w=2x + 4\) into \(2l + 2w\).
We get \(2(8x - 1)+2(2x + 4)\).

Step2: Distribute 2

Using the distributive property \(a(b + c)=ab+ac\), for \(2(8x - 1)\), we have \(2\times8x-2\times1 = 16x-2\), and for \(2(2x + 4)\), we have \(2\times2x+2\times4=4x + 8\).

Step3: Combine like - terms

\((16x-2)+(4x + 8)=(16x+4x)+(-2 + 8)\)
\(=20x+6\)

Answer:

The perimeter of the rectangle is \(20x + 6\) inches.