College Algebra 7th Edition

Published by Brooks Cole
ISBN 10: 1305115546
ISBN 13: 978-1-30511-554-5

Chapter P, Prerequisites - Chapter P Review - Exercises - Page 77: 73


$x + (2x-1)\sqrt{x}$

Work Step by Step

Multiply $\sqrt{x}$ to each term of $(\sqrt{x}+1)$ to obtain: $=(\sqrt{x} \cdot \sqrt{x} + \sqrt{x}\cdot 1)(2\sqrt{x}-1) \\=(x+\sqrt{x})(2\sqrt{x}-1)$ Multiply using the formula $(a+b)(c+d) = ac + ad + bc + bd$ or the FOIL method, to obtain: $=x(2\sqrt{x}) + x(-1) + \sqrt{x}(2\sqrt{x})+\sqrt{x}(-1) \\=2x\sqrt{x}-x+2x-\sqrt{x}$ Combine like terms to obtain: $=(-x+2x) + (2x\sqrt{x}-\sqrt{x}) \\=x +\sqrt{x}(2x-1) \\=x + (2x-1)\sqrt{x}$
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