Answer
1. Using FOIL:
$= xy + xz + y^{2} + yz$
2. Comparison with small plot areas:
The product found in 1. is the sum of all these four small areas.
Work Step by Step
1. Use FOIL to complete multiplication
$= (x+y)(y + z)$
$= x(y+z) + y(y +z)$
$= xy + xz + y^{2} + yz$
2. Find the area of each of the four smaller plots
2.1 Darkest green plot area
$= y \times y$
$= y^{2}$
2.2 2nd darkest green plot area
$= x \times y$
$= xy$
2.3 Green plot area
$= y \times z$
$= yz$
2.4 Light green plot area
$= x \times z$
$= xz$
So we get the areas of: $y^{2}, xy, yz, xz$
The product found in 1. is the sum of all these four small areas.
