Question

Use models to prove that 3(a+b) is equivalent to 3a + 3b

Answer 1

Method One: "Plug-in Method"
To do this, you could plug in two numbers for a and b to check that they get the same value:

`a=2,b=3 \\ 3(a+b); 3a+3b \\ 3(2+3); 3(2)+3(3) \\ 3(5); 6+9 \\ 15; 15 \\ 15=15`
Therefore:
3(a+b)=3a+3b

Method Two: "Setting Equal Method"
By setting the two statements equal to each other, you can see they are the same because everything cancels out

`3(a+b) = 3a+3b \\ (3(a+b)=3a+3b)/(3) \\ a+b=a+b \\ a+b-a=a+b-a \\ b=b \\ b-b=b-b \\ 0=0`

*Keep in mind these aren't theoretical names, simply what I'm calling my two methods!

I hope this helps!!