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Precalculus Enhanced with Graphing Utilities

Sullivan

$Math Studyset 91影视 Explanations$ Math

6th Edition 路 1200 pages

ISBN: 9780321795465

Chapter 12: Q. 13 (page 839)

Expand ${(3 m + 2)}^{5}$ using the Binomial Theorem.

Short Answer

Expert verified

Thus, ${(3 m + 2)}^{5} = 243 m^{5} + 810 m^{4} + 1080 m^{3} + 720 m^{2} + 240 m + 32$

Step by step solution

01

Step 1. Given Information

The given polynomial is ${(3 m + 2)}^{5}$ .

In the binomial Theorem, let role="math" localid="1646973173648" $a = 3 m, n = 5$ .

02

Step 2. Expand Polynomial

${(3 m + 2)}^{5} = {}^{5}C_{0} {(3 m)}^{5} 2^{0} + {}^{5}C_{1} {(3 m)}^{4} 2^{1} + {}^{5}C_{2} {(3 m)}^{3} 2^{2} + {}^{5}C_{3} {(3 m)}^{2} 2^{3} + {}^{5}C_{4} (3 m) 2^{4} + {}^{5}C_{5} 2^{5} {(3 m + 2)}^{5} = 1 (243 m^{5}) + 5 (81 m^{4}) 2 + 10 (27 m^{3}) 4 + 10 (9 m^{2}) 8 + 5 (3 m) 16 + 1 (32) {(3 m + 2)}^{5} = 243 m^{5} + 810 m^{4} + 1080 m^{3} + 720 m^{2} + 240 m + 32$

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