Chapter 5 - Section 5.4 - Multiplying Polynomials - Exercise Set - Page 290: 101

$30x^2y^{2n+1}-10x^2y^n$

Using $a(b+c)=ab+ac$ or the Distributive Property and using the laws of exponents, the given expression, $ 5x^2y^n(6y^{n+1}-2) $, simplifies to \begin{array}{l}\require{cancel} 30x^2y^{n+n+1}-10x^2y^n \\\\= 30x^2y^{2n+1}-10x^2y^n .\end{array}