Intermediate Algebra (6th Edition)

Published by Pearson
ISBN 10: 0321785045
ISBN 13: 978-0-32178-504-6

Chapter 5 - Section 5.4 - Multiplying Polynomials - Exercise Set - Page 289: 39



Work Step by Step

Using the square of a binomial, $(a+b)^2=a^2+2(a)(b)+b^2$, the given expression is equivalent to \begin{align*} & [3+(4b+1)]^2 \\\\& 3^2+2(3)(4b+1)+(4b+1)^2 \\\\& 9+24b+6+(4b+1)^2 \\\\& 24b+15+(4b+1)^2 \\\\& 24b+15+(4b)^2+2(4b)(1)+1^2 \\\\& 24b+15+16b^2+8b+1 \\\\& 16b^2+(24b+8b)+(15+1) \\\\& 16b^2+32b+16 .\end{align*}
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