Chapter 1 - Introduction to Algebraic Expressions - 1.2 The Commutative, Associative, and Distributive Laws - 1.2 Exercise Set - Page 18: 93

Distributive Associative Commutative Associative Distributive

$[2(x+1)]+3x$ The $2$ is multiplied by $x$ and $1$, showing the DISTRIBUTIVE property, which states that if one term is being multiplied by an expression, the first term is multiplied by the terms grouped together. ($a(b+c)=ab+ac$) $[2\times x+2\times1]+3x$ $[2x+2]+3x$ The brackets are moved to be around $2+3x$ instead of $2x+2$, showing the ASSOCIATIVE property, which states that the grouping of an addition expression doesn't change the value. ($(a+b)+c$) $2x+[2+3x]$ $2$ and $3x$ are switched around, showing the COMMUTATIVE property, which states that the order of a multiplication expression doesn't change the value. ($ab=ba$) $2x+[3x+2]$ The brackets are moved to group $2x$ and $3x$ instead of $3x$ and $2$. That shows the ASSOCIATIVE property, which states the order of an addition expression doesn't change the value ($a+(b+c)=(a+b)+c$). $[2x+3x]+2$ It is shown that $x$ goes into both $2x$ and $3x$. This is the DISTRIBUTIVE property because it creates a $a(b+c)$ expression. ($(ab+ac)=a(b+c)$. $[(2+3)x]+2$ $[5x]+2$ $5x+2$