Question 210108
{{{5(x+3)=5x+5(3)=5x+15}}}



So {{{5(x+3)=5x+15}}}



This is the distributive property at work.



Why does this property work? Here's an easier example:


The expression {{{3(x+y)}}} is the same as {{{(x+y)+(x+y)+(x+y)}}}. In other words, there are 3 groups of 'x+y' being added together (that's basically what multiplication means). 


So {{{3(x+y)=(x+y)+(x+y)+(x+y)=(x+x+x)+(y+y+y)=3x+3y}}}


To save us the trouble of repeated adding, we simply multiply. For example, you could add up the terms of {{{10(x+y)}}}, but this gets tedious after a while.