Question

What is the area of a rectangle with a height of t ^ 2 + 7t + 6 and a width of 2t + 1 .

Answer 1

For this case we have that by definition, the area of a rectangle is given by:

$A = a * b$

Where:

a: It is the length of the rectangle

b: It is the width of the rectangle

According to the statement we have:

$a = t ^ 2 + 7t + 6\\b = 2t + 1$

Substituting we have:

$A = (t ^ 2 + 7t + 6) (2t + 1)$

We apply distributive property:

$A = 2t ^ 3 + t ^ 2 + 14t ^ 2 + 7t + 12t + 6$

We add similar terms:

$A = 2t ^ 3 + 15t ^ 2 + 19t + 6$

Answer:

$A = 2t ^ 3 + 15t ^ 2 + 19t + 6$