Elementary Geometry for College Students (6th Edition)

Published by Brooks Cole
ISBN 10:
ISBN 13:

Appendix A - A.1 - Algebraic Expressions - Exercises - Page 535: 30

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.
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