Answer:
[tex]=16ax+32ay-12bx-24by[/tex]
Step-by-step explanation:
[tex]16a\left(x+2y\right)-12b\left(x+2y\right)\\\mathrm{Expand}\:16a\left(x+2y\right):\quad 16ax+32ay\\16a\left(x+2y\right)\\\mathrm{Apply\:the\:distributive\:law}:\quad \:a\left(b+c\right)=ab+ac\\a=16a,\:b=x,\:c=2y\\=16ax+16a\cdot \:2y\\=16ax+16\cdot \:2ay\\\mathrm{Multiply\:the\:numbers:}\:16\cdot \:2=32\\=16ax+32ay\\=16ax+32ay-12b\left(x+2y\right)\\\mathrm{Expand}\:-12b\left(x+2y\right):\quad -12bx-24by\\-12b\left(x+2y\right)\\\mathrm{Apply\:the\:distributive\:law}:\quad \:a\left(b+c\right)=ab+ac[/tex]
[tex]a=-12b,\:b=x,\:c=2y\\=-12bx+\left(-12b\right)\cdot \:2y\\Apply\:minus-plus\:rules\\+\left(-a\right)=-a\\=-12bx-12\cdot \:2by\\\mathrm{Multiply\:the\:numbers:}\:12\cdot \:2=24\\=-12bx-24by\\=16ax+32ay-12bx-24by[/tex]
