Respuesta :

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]