Question

The figures below are squares. Find an expression for the area of each shaded region. Write your answers in standard form.

The bigger square is x+3 on all 3 sides.
The smaller square is x on every side.

Answer 1

Given:
Big square: side length = x + 3
Small square: side length = x

Area of a square = a²    where a represents the side length.

Area of big square = (x+3)²
A = (x+3)(x+3) 
A = x(x+3) + 3(x+3)
A = x² + 3x + 3x + 9
A = x² + 6x + 9

Area of small square = x²

Total Area = Area of Big square + Area of Small square
Total Area = x² + 6x + 9 + x²
Total Area = 2x² + 6x + 9