The problem in the image asks to find the area of a rectangle, where the dimensions are given as $x + 6$ and $x + 1$.

Step-by-Step Solution:

The formula for the area $A$ of a rectangle is:

$A = \text{length} \times \text{width}$

Here, the length is $x + 6$ and the width is $x + 1$.

So, the area $A$ can be written as:

$A = (x + 6)(x + 1)$

Now, expand this expression using the distributive property (also known as the FOIL method):

$A = (x + 6)(x + 1) = x(x + 1) + 6(x + 1)$

Expanding each term:

$A = x^2 + x + 6x + 6$

Combine like terms:

$A = x^2 + 7x + 6$

Thus, the area of the rectangle is:

$A = x^2 + 7x + 6$

This is the simplified expression for the area.

Would you like further clarification on any step?

Here are 5 related questions for practice:

1. What is the area of the rectangle if $x = 3$?
2. How would the area change if the dimensions were $x + 5$ and $x + 2$?
3. What are the steps for factoring the area expression $x^2 + 7x + 6$?
4. How can you graph the equation $A = x^2 + 7x + 6$ to visualize the area?
5. If the perimeter of the rectangle is required, how would you calculate it?

Tip: Always double-check your algebraic expansions and combine like terms carefully to avoid mistakes.