Introductory Algebra for College Students (7th Edition)

Published by Pearson
ISBN 10: 0-13417-805-X
ISBN 13: 978-0-13417-805-9

Chapter 5 - Review Exercises - Page 415: 43


The area of the rectangle is $x^2 + 7x + 12$.

Work Step by Step

The formula for the area of a rectangle is given by the formula: $$A = lw$$ According to the diagram presented, the length can be given by the following expression: $$l = x + 4$$ Also according to the diagram, the width is given by the following expression: $$w = x + 3$$ With these expressions, we can plug these in for $l$ and $w$ into the equation for the area of a rectangle: $$A = (x + 4)(x + 3)$$ We can use the FOIL method to multiply the two binomials together and expand the expression. In the FOIL method, we first multiply the first terms, then the outside terms, then the inside terms, and, finally, the last terms: $$A = (x)(x) + (3)(x) + (4)(x) + (4)(3)$$ Now, we multiply to simplify: $$A = x^2 + 3x + 4x + 12$$ Combine like terms to simplify the equation: $$A = x^2 + 7x + 12$$
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