For this case we have that by definition, the area of a rectangle is given by:
[tex]A = a * b[/tex]
Where:
a: It is the length of the rectangle
b: It is the width of the rectangle
According to the statement we have:
[tex]a = t ^ 2 + 7t + 6\\b = 2t + 1[/tex]
Substituting we have:
[tex]A = (t ^ 2 + 7t + 6) (2t + 1)[/tex]
We apply distributive property:
[tex]A = 2t ^ 3 + t ^ 2 + 14t ^ 2 + 7t + 12t + 6[/tex]
We add similar terms:
[tex]A = 2t ^ 3 + 15t ^ 2 + 19t + 6[/tex]
Answer:
[tex]A = 2t ^ 3 + 15t ^ 2 + 19t + 6[/tex]