Chapter 5 - Section 5.2 - Multiplying Polynomials - Exercise Set - Page 360: 103

See the explanation

a. $A=l\times w$ $l=2x+1, w=x+2$ $A=(2x+1)(x+2)$ b. $A_{1}=l_{1}w_{1}=2x(x)=2x^2$ $A_{2}=l_{2}w_{2}=1(x)=x$ $A_{3}=l_{3}w_{3}=2x(2)=4x$ $A_{4}=l_{4}w_{4}=1(2)=2$ $A_{T}=2x^2+x+4x+2=2x^2+5x+2,$ c. $A=(2x+1)(x+2),$ $=2x^2+4x+x+2,$ $=2x^2+5x+2,$ Thus, Areas in part (a) and part (b) are equal.