College Algebra (11th Edition)

Published by Pearson
ISBN 10: 0321671791
ISBN 13: 978-0-32167-179-0

Chapter 1 - Review Exercises - Page 163: 28



Work Step by Step

Using $(a+b)(c+d)=ac+ad+bc+bd$ or the FOIL Method and using $i^2=-1$, the given expression $ 4i(2+5i)(2-i) ,$ simplifies to \begin{array}{l}\require{cancel} 4i[2(2)+2(-i)+5i(2)+5i(-i)] \\\\= 4i[4-2i+10i-5i^2] \\\\= 4i[4-2i+10i-5(-1)] \\\\= 4i[4-2i+10i+5] \\\\= 4i[(4+5)+(-2i+10i)] \\\\= 4i[9+8i] \\\\= 36i+32i^2 \\\\= 36i+32(-1) \\\\= 36i-32 \\\\= -32+36i .\end{array}
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