Chapter 12 - Sequences; Induction; the Binomial Theorem - Chapter Review - Chapter Test - Page 840: 13

$243m^5+810m^4+1080m^3+720m^2+240m+32$

Work Step by Step

We are given the expression: $(3m+2)^5$ Expand the expression using the Binomial Theorem: $(3m+2)^5=\binom{5}{0}(3m)^52^0+\binom{5}{1}(3m)^42^1+\binom{5}{2}(3m)^32^2+\binom{5}{3}(3m)^22^3+\binom{5}{4}(3m)^12^4+\binom{5}{5}(3m)^02^5$ $=243m^5+5(81)m^4(2)+10(27)m^3(4)+10(9)m^2(8)+5(3)m(16)+32$ $=243m^5+810m^4+1080m^3+720m^2+240m+32$

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