## Elementary Algebra

$13x+22y$
Using $a(b+c)=ab+ac$, or the Distributive Property, and then combining like terms, the given expression, $5(x+2y)+4(2x+3y) ,$ simplifies to \begin{array}{l}\require{cancel} 5x+10y+8x+12y \\\\= (5x+8x)+(10y+12y) \\\\= 13x+22y .\end{array}