College Algebra 7th Edition

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

Chapter 8, Sequences and Series - Section 8.6 - The Binomial Theorem - 8.6 Exercises: 28

Answer

$(2A+B^{2})^{4}=16A^{4}+32A^{3}B^{2}+24A^{2}B^{4}+8AB^{6}+B^{8}$

Work Step by Step

We expand using the Binomial Theorem: $(2A+B^{2})^{4}=\left(\begin{array}{l} 4\\ 0 \end{array}\right)(2A)^{4}+\left(\begin{array}{l} 4\\ 1 \end{array}\right)(2A)^{3}(B^{2})^{1}+\left(\begin{array}{l} 4\\ 2 \end{array}\right)(2A)^{2}(B^{2})^{2}+\left(\begin{array}{l} 4\\ 3 \end{array}\right)(2A)^{1}(B^{2})^{3}+\left(\begin{array}{l} 4\\ 4 \end{array}\right)(B^{2})^{4}=1*16A^4+4*8A^3B^2+6*4A^2B^4+4*2AB^6+1*B^8=16A^{4}+32A^{3}B^{2}+24A^{2}B^{4}+8AB^{6}+B^{8}$
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