Question

the area of the figure to the right is (x + 2)(x + 3). find another expression for this area by finding the sum of the areas of the smaller rectangles. the area is □. (simplify your answer.)

Explanation:

Step1: Identify the four rectangles

The figure can be divided into four smaller rectangles. Their dimensions are: \(x \times x\), \(x \times 3\), \(2 \times x\), and \(2 \times 3\).

Step2: Calculate the area of each rectangle

• Area of \(x \times x\): \(x \times x = x^2\)
• Area of \(x \times 3\): \(x \times 3 = 3x\)
• Area of \(2 \times x\): \(2 \times x = 2x\)
• Area of \(2 \times 3\): \(2 \times 3 = 6\)

Step3: Sum the areas of the rectangles

Add the four areas together: \(x^2 + 3x + 2x + 6\)

Step4: Combine like terms

Combine the \(x\)-terms: \(x^2 + (3x + 2x) + 6 = x^2 + 5x + 6\)

Answer:

\(x^2 + 5x + 6\)