Question

the area of a rectangle
find a completely simplified expression for the area (length x width) of the (blue) shaded rectangle:

$4x + 5$

$4x - 5$

area =

Explanation:

Step1: Recall area formula

The area of a rectangle is \( A = \text{length} \times \text{width} \). Here, length is \( 4x + 5 \) and width is \( 4x - 5 \).

Step2: Apply difference of squares

Use the formula \( (a + b)(a - b) = a^2 - b^2 \), where \( a = 4x \) and \( b = 5 \).
So, \( (4x + 5)(4x - 5) = (4x)^2 - 5^2 \).

Step3: Simplify the terms

Calculate \( (4x)^2 = 16x^2 \) and \( 5^2 = 25 \).
Thus, the expression becomes \( 16x^2 - 25 \).

Answer:

\( 16x^2 - 25 \)