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Explanation:
The distributive property is [tex]a(b+c) = ab+ac[/tex]
We multiply the outer term 'a' by each term inside the parenthesis.
In the example of 3(x+2), we multiply the outer term 3 with each term inside the parenthesis.
That's how we go from 3(x+2) to 3x+6
Another way to think of it is to think of 3(x+2) as three copies of (x+2) being added. So,
(x+2)+(x+2)+(x+2) = (x+x+x) + (2+2+2) = 3x+6
The distribution rule is the shortcut of repeated addition like this.
[tex]\huge\text{\bf Hey there!}[/tex]
[tex]\large\textsf{FORMULAS for you to follow}\\\\\large\text{Associative Property}\\\large\textsf{(a + b) + c = a + (b + c)}\\\\\large\text{Cummutative Property}\\\large\textsf{a + b = b + a}\\\\\large\text{Additive Identity Property}\\\large\textsf{a + 0 = 0 + a = a}\\\\\large\text{Distributive Property}\\\large\textsf{a(b + c) = a(b) + a(c) = ab + ac}[/tex]
[tex]\large\textsf{3(x + 2)}\\\large\textsf{= 3(x) + 3(2)}\\\large\textsf{= 3x + 6}[/tex]
[tex]\huge\text{Thus, your answer is: \boxed{\textsf{Distributive Property}}}\huge\checkmark\\\\\large\text{Reason: because you're basically DISTRIBUTING 3 within the}\\\large\text{parentheses.}[/tex]
[tex]\huge\text{\bf Good luck on your assignment \&}\\\huge\text{\bf enjoy your day!}[/tex]