Question

the area of the entire rectangle to the right is x(x + 4). find another expression for this area by finding the sum of the areas of the smaller rectangles. the area is □.

Explanation:

Step1: Identify the two smaller rectangles

The entire rectangle can be divided into two smaller rectangles: one with dimensions \( x \) and \( x \), and the other with dimensions \( x \) and \( 4 \).

Step2: Calculate the area of each small rectangle

• Area of the first (purple) rectangle: \( \text{length} \times \text{width} = x \times x = x^2 \)
• Area of the second (blue) rectangle: \( \text{length} \times \text{width} = x \times 4 = 4x \)

Step3: Sum the areas of the two smaller rectangles

To find the area of the entire rectangle, we add the areas of the two smaller rectangles: \( x^2 + 4x \)

We can also verify this by expanding the given expression \( x(x + 4) \) using the distributive property (also known as the distributive law of multiplication over addition):

$$ x(x + 4) = x \times x + x \times 4 = x^2 + 4x $$

Answer:

\( x^2 + 4x \)