# Chapter 11 - Further Topics in Algebra - 11.4 The Binomial Theorem - 11.4 Exercises - Page 1045: 35

$r^{10} + 5 r^8 s + 10 r^6 s^2 + 10 r^4 s^3 + 5 r^2 s^4 + s^5$

#### Work Step by Step

$(x+y)^n=\binom{n}{0}x^ny^0+\binom{n}{1}x^{n-1}y^1+...+\binom{n}{a}x^{n-a}y^a+..\binom{n}{n}x^{0}y^n$ Here: $n=7$, $(r^2+s)^5=\binom{5}{0}(r^2)^7s^0+\binom{5}{1}(r^2)^{5-1}s^1+\binom{5}{2}(r^2)^{5-2}s^2+\binom{5}{3}(r^2)^{5-3}s^3+\binom{5}{4}(r^2)^{5-4}s^4+\binom{5}{5}(r^2)^{5-5}s^5=$ $r^{10} + 5 r^8 s + 10 r^6 s^2 + 10 r^4 s^3 + 5 r^2 s^4 + s^5$

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