Question

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Explanation:

Assuming the problem is to find the area of the shaded region (the large square minus the small square), we can use the formula for the area of a square (\(A = s^2\)) and then subtract the areas.

Step 1: Find the area of the large square

The side length of the large square is \(5x + 3\). The area of a square is side length squared, so:
\(A_{large}=(5x + 3)^2\)
Expanding \((5x + 3)^2\) using the formula \((a + b)^2=a^2+2ab + b^2\) where \(a = 5x\) and \(b = 3\):
\(A_{large}=(5x)^2+2(5x)(3)+3^2=25x^2 + 30x+9\)

Step 2: Find the area of the small square

The side length of the small square is \(2x - 3\). The area of the small square is:
\(A_{small}=(2x - 3)^2\)
Expanding \((2x - 3)^2\) using the formula \((a - b)^2=a^2-2ab + b^2\) where \(a = 2x\) and \(b = 3\):
\(A_{small}=(2x)^2-2(2x)(3)+3^2=4x^2-12x + 9\)

Step 3: Find the area of the shaded region (large - small)

Subtract the area of the small square from the area of the large square:
\(A = A_{large}-A_{small}=(25x^2 + 30x + 9)-(4x^2-12x + 9)\)
Simplify the expression:
\(A=25x^2+30x + 9 - 4x^2 + 12x-9\)
Combine like terms:
\(A=(25x^2-4x^2)+(30x + 12x)+(9 - 9)\)
\(A = 21x^2+42x\)

Answer:

The area of the shaded region is \(21x^2 + 42x\)