Final answer:
The expression 9x - 81 can be factored by taking out the common factor of 9, resulting in the expression 9(x - 9), which is option b).
Step-by-step explanation:
The question asks to rewrite the expression 9x - 81 using a common factor. The common factor in both terms is 9, so we can factor out the 9 and rewrite the expression as 9(x - 9). This corresponds to option b) 9(x-9).
To demonstrate how the factoring works, you can consider the distributive property of multiplication over addition, which states that a(b + c) = ab + ac. In this case, if you distribute the 9 inside the parentheses of 9(x - 9), you would get 9x - 81, which is the original expression. So, factoring the common factor of 9 turns 9x - 81 into 9(x - 9).