Final answer:
Use the distributive property to factor out the common factor of 9 from the terms 84 and 34, resulting in 9(84 - 34), and simplify by subtraction and multiplication to get the final answer of 450.
Step-by-step explanation:
To apply the distributive property to the expression 84 x 9 - 34 x 9, we will distribute the 9 across the terms that are being subtracted. The distributive property tells us that a(b + c) = ab + ac, and this rule can also be applied in reverse for subtraction: a(b - c) = ab - ac.
So for your expression, we can factor out the common factor of 9:
9 (84 - 34).
Now we just need to perform the subtraction inside the parentheses:
9 (84 - 34) = 9 (50).
Finally, multiply 9 by 50 to get the result:
9 x 50 = 450.