The area of a rectangle with length l and width w is given by l x w = lw.
Consider a rectangle with length (l + 3) and width w. Then the area is
w x (l + 3)
= w (l + 3)
= lw + 3w
This is the sum of the areas of the two smaller rectangles as shown in the figure:
Similarly,the area of a rectangle with length (p + q) and the width w is given by w(p + q)
Also, w(p + q) = pw + qw
(p + q)w = pw + qw.
This is known as the distributive property of multiplication over addition.
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