Answer:
(d) 2np +P²
Explanation:
The area of a square is the square of its side dimensions. The difference in area can be found by subtracting the smaller square's area from that of the larger square.
Area
For side length s, the area is ...
A = s²
Larger square:
(n +p)² = n² +2np +p²
Smaller square:
n²
Difference in area
The large square is larger by ...
(n +p)² -n²
= n² +2np +p² -n²
= 2np +p² . . . . . . large square has greater area by this amount
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Additional comment
If you extend the sides of the white square, you see they divide the overall area into 4 parts. The white square has dimensions n×n. The upper left and lower right rectangles have dimensions n×p, so their total area is 2np. The upper right square has dimensions p×p, so its area is p².
The total blue area is 2np+p², the amount by which the large square's area exceeds that of the small (white) square.